# A+ Answers - Gauss Jordan elimination

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x - 2y + z = 0

y - 3z = -1

2y + 5z = -2

A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}

Question 2 of 40

use Cramer’s Rule to solve the following system.

x + y + z = 0

2x - y + z = -1

-x + 3y - z = -8

A. {(-1, -3, 7)}

B. {(-6, -2, 4)}

C. {(-5, -2, 7)}

D. {(-4, -1, 7)}

Question 3 of 40

use Gauss-Jordan elimination to solve the system.

-x - y - z = 1

4x + 5y = 0

y - 3z = 0

A. {(14, -10, -3)}

B. {(10, -2, -6)}

C. {(15, -12, -4)}

D. {(11, -13, -4)}

Question 4 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

2x = 3y + 2

5x = 51 - 4y

A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

Question 5 of 40

use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w - 2x - y - 3z = -9

w + x - y = 0

3w + 4x + z = 6

2x - 2y + z = 3

A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 6 of 40

Use Cramer’s Rule to solve the following system.

x + y = 7

x - y = 3

A. {(7, 2)}

B. {(8, -2)}

C. {(5, 2)}

D. {(9, 3)}

Question 7 of 40

Use Cramer’s Rule to solve the following system.

3x - 4y = 4

2x + 2y = 12

A. {(3, 1)}

B. {(4, 2)}

C. {(5, 1)}

D. {(2, 1)}

Question 8 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y + z = 4

x - y - z = 0

x - y + z = 2

A. {(3, 1, 0)}

B. {(2, 1, 1)}

C. {(4, 2, 1)}

D. {(2, 1, 0)}

Question 9 of 40

Find values for x, y, and z so that the following matrices are equal.

2x

z y + 7

4 = -10

6 13

4

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

Question 10 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

4x - 5y - 6z = -1

x - 2y - 5z = -12

2x - y = 7

A. {(2, -3, 4)}

B. {(5, -7, 4)}

C. {(3, -3, 3)}

D. {(1, -3, 5)}

Question 11 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2

2x - y + z = 5

-x + 2y + 2z = 1

A. {(0, -1, -2)}

B. {(2, 0, 2)}

C. {(1, -1, 2)}

D. {(4, -1, 3)}

Question 12 of 40

Use Cramer’s Rule to solve the following system.

12x + 3y = 15

2x - 3y = 13

A. {(2, -3)}

B. {(1, 3)}

C. {(3, -5)}

D. {(1, -7)}

Question 13 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

8x + 5y + 11z = 30

-x - 4y + 2z = 3

2x - y + 5z = 12

A. {(3 - 3t, 2 + t, t)}

B. {(6 - 3t, 2 + t, t)}

C. {(5 - 2t, -2 + t, t)}

D. {(2 - 1t, -4 + t, t)}

Question 14 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to each system.

2x + 3y - 5z = 15

x + 2y - z = 4

A. {(6t + 28, -7t - 6, t)}

B. {(7t + 18, -3t - 7, t)}

C. {(7t + 19, -1t - 9, t)}

D. {(4t + 29, -3t - 2, t)}

Question 15 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

5x + 8y - 6z = 14

3x + 4y - 2z = 8

x + 2y - 2z = 3

A. {(-4t + 2, 2t + 1/2, t)}

B. {(-3t + 1, 5t + 1/3, t)}

C. {(2t + -2, t + 1/2, t)}

D. {(-2t + 2, 2t + 1/2, t)}

Question 16 of 40

Solve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 8

2x + 7y + 6z =10

2x + 7y + 7z = 9

The inverse of:

2

2

2 6

7

7 6

6

7

is

7/2

-1

0 0

1

-1 -3

0

1

A. {(1, 2, -1)}

B. {(2, 1, -1)}

C. {(1, 2, 0)}

D. {(1, 3, -1)}

Question 17 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

2w + x - y = 3

w - 3x + 2y = -4

3w + x - 3y + z = 1

w + 2x - 4y - z = -2

A. {(1, 3, 2, 1)}

B. {(1, 4, 3, -1)}

C. {(1, 5, 1, 1)}

D. {(-1, 2, -2, 1)}

Question 18 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 2y = z - 1

x = 4 + y - z

x + y - 3z = -2

A. {(3, -1, 0)}

B. {(2, -1, 0)}

C. {(3, -2, 1)}

D. {(2, -1, 1)}

Question 19 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

x + 2y + 2z = 5

2x + 4y + 7z = 19

-2x - 5y - 2z = 8

A. {(33, -11, 4)}

B. {(13, 12, -3)}

C. {(23, -12, 3)}

D. {(13, -14, 3)}

Question 20 of 40

Use Cramer’s Rule to solve the following system.

4x - 5y = 17

2x + 3y = 3

A. {(3, -1)}

B. {(2, -1)}

C. {(3, -7)}

D. {(2, 0)}

Part 2 of 2 - Lesson 7 Questions 20.0/ 50.0 Points

Question 21 of 40

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 1)2 = -8x

A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2

B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3

C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1

D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5

Question 22 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1

B. (x - 1)2/18 + (y + 2)2/71 = 1

C. (x - 1)2/16 + (y + 2)2/9 = 1

D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 23 of 40

2.5/ 2.5 Points

Find the focus and directrix of the parabola with the given equation.

8x2 + 4y = 0

A. Focus: (0, -1/4); directrix: y = 1/4

B. Focus: (0, -1/6); directrix: y = 1/6

C. Focus: (0, -1/8); directrix: y = 1/8

D. Focus: (0, -1/2); directrix: y = 1/2

Question 24 of 40

Locate the foci and find the equations of the asymptotes.

x2/100 - y2/64 = 1

A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x

B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x

C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x

D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x

Question 25 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (0, -3), (0, 3)

Vertices: (0, -1), (0, 1)

A. y2 - x2/4 = 0

B. y2 - x2/8 = 1

C. y2 - x2/3 = 1

D. y2 - x2/2 = 0

Question 26 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

x2 - 2x - 4y + 9 = 0

A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1

B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3

C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1

D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5

Question 27 of 40

2.5/ 2.5 Points

Find the vertices and locate the foci of each hyperbola with the given equation.

x2/4 - y2/1 =1

A.

Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)

B.

Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)

C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)

D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)

Question 28 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1

B. (x - 2)2/24 + (y + 1)2/36 = 1

C. (x - 2)2/35 + (y + 1)2/25 = 1

D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 29 of 40

Convert each equation to standard form by completing the square on x and y.

4x2 + y2 + 16x - 6y - 39 = 0

A. (x + 2)2/4 + (y - 3)2/39 = 1

B. (x + 2)2/39 + (y - 4)2/64 = 1

C. (x + 2)2/16 + (y - 3)2/64 = 1

D. (x + 2)2/6 + (y - 3)2/4 = 1

Question 30 of 40

2.5/ 2.5 Points

Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 31 of 40

2.5/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x + 1)2 = -8(y + 1)

A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1

B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1

C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1

D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1

Question 32 of 40

Find the vertices and locate the foci of each hyperbola with the given equation.

y2/4 - x2/1 = 1

A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)

B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)

C.

Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)

D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)

Question 33 of 40

2.5/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x - 2)2 = 8(y - 1)

A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1

B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1

C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1

D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1

Question 34 of 40

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)

Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1

B. (x - 7)2/5 + (y - 6)2/6 = 1

C. (x - 7)2/4 + (y - 6)2/9 = 1

D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 35 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (0, -4), (0, 4)

Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 36 of 40

Find the focus and directrix of each parabola with the given equation.

x2 = -4y

A. Focus: (0, -1), directrix: y = 1

B. Focus: (0, -2), directrix: y = 1

C. Focus: (0, -4), directrix: y = 1

D. Focus: (0, -1), directrix: y = 2

Question 37 of 40

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9

B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6

C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6

D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8

Question 38 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-5, 0), (5, 0)

Vertices: (-8, 0), (8, 0)

A. x2/49 + y2/ 25 = 1

B. x2/64 + y2/39 = 1

C. x2/56 + y2/29 = 1

D. x2/36 + y2/27 = 1

Question 39 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-2, 0), (2, 0)

Y-intercepts: -3 and 3

A. x2/23 + y2/6 = 1

B. x2/24 + y2/2 = 1

C. x2/13 + y2/9 = 1

D. x2/28 + y2/19 = 1

Question 40 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Endpoints of transverse axis: (0, -6), (0, 6)

Asymptote: y = 2x

A. y2/6 - x2/9 = 1

B. y2/36 - x2/9 = 1

C. y2/37 - x2/27 = 1

D. y2/9 - x2/6 = 1

x - 2y + z = 0

y - 3z = -1

2y + 5z = -2

A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}

Question 2 of 40

use Cramer’s Rule to solve the following system.

x + y + z = 0

2x - y + z = -1

-x + 3y - z = -8

A. {(-1, -3, 7)}

B. {(-6, -2, 4)}

C. {(-5, -2, 7)}

D. {(-4, -1, 7)}

Question 3 of 40

use Gauss-Jordan elimination to solve the system.

-x - y - z = 1

4x + 5y = 0

y - 3z = 0

A. {(14, -10, -3)}

B. {(10, -2, -6)}

C. {(15, -12, -4)}

D. {(11, -13, -4)}

Question 4 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

2x = 3y + 2

5x = 51 - 4y

A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

Question 5 of 40

use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w - 2x - y - 3z = -9

w + x - y = 0

3w + 4x + z = 6

2x - 2y + z = 3

A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 6 of 40

Use Cramer’s Rule to solve the following system.

x + y = 7

x - y = 3

A. {(7, 2)}

B. {(8, -2)}

C. {(5, 2)}

D. {(9, 3)}

Question 7 of 40

Use Cramer’s Rule to solve the following system.

3x - 4y = 4

2x + 2y = 12

A. {(3, 1)}

B. {(4, 2)}

C. {(5, 1)}

D. {(2, 1)}

Question 8 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y + z = 4

x - y - z = 0

x - y + z = 2

A. {(3, 1, 0)}

B. {(2, 1, 1)}

C. {(4, 2, 1)}

D. {(2, 1, 0)}

Question 9 of 40

Find values for x, y, and z so that the following matrices are equal.

2x

z y + 7

4 = -10

6 13

4

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

Question 10 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

4x - 5y - 6z = -1

x - 2y - 5z = -12

2x - y = 7

A. {(2, -3, 4)}

B. {(5, -7, 4)}

C. {(3, -3, 3)}

D. {(1, -3, 5)}

Question 11 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2

2x - y + z = 5

-x + 2y + 2z = 1

A. {(0, -1, -2)}

B. {(2, 0, 2)}

C. {(1, -1, 2)}

D. {(4, -1, 3)}

Question 12 of 40

Use Cramer’s Rule to solve the following system.

12x + 3y = 15

2x - 3y = 13

A. {(2, -3)}

B. {(1, 3)}

C. {(3, -5)}

D. {(1, -7)}

Question 13 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

8x + 5y + 11z = 30

-x - 4y + 2z = 3

2x - y + 5z = 12

A. {(3 - 3t, 2 + t, t)}

B. {(6 - 3t, 2 + t, t)}

C. {(5 - 2t, -2 + t, t)}

D. {(2 - 1t, -4 + t, t)}

Question 14 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to each system.

2x + 3y - 5z = 15

x + 2y - z = 4

A. {(6t + 28, -7t - 6, t)}

B. {(7t + 18, -3t - 7, t)}

C. {(7t + 19, -1t - 9, t)}

D. {(4t + 29, -3t - 2, t)}

Question 15 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

5x + 8y - 6z = 14

3x + 4y - 2z = 8

x + 2y - 2z = 3

A. {(-4t + 2, 2t + 1/2, t)}

B. {(-3t + 1, 5t + 1/3, t)}

C. {(2t + -2, t + 1/2, t)}

D. {(-2t + 2, 2t + 1/2, t)}

Question 16 of 40

Solve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 8

2x + 7y + 6z =10

2x + 7y + 7z = 9

The inverse of:

2

2

2 6

7

7 6

6

7

is

7/2

-1

0 0

1

-1 -3

0

1

A. {(1, 2, -1)}

B. {(2, 1, -1)}

C. {(1, 2, 0)}

D. {(1, 3, -1)}

Question 17 of 40

2.5/ 2.5 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

2w + x - y = 3

w - 3x + 2y = -4

3w + x - 3y + z = 1

w + 2x - 4y - z = -2

A. {(1, 3, 2, 1)}

B. {(1, 4, 3, -1)}

C. {(1, 5, 1, 1)}

D. {(-1, 2, -2, 1)}

Question 18 of 40

2.5/ 2.5 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + 2y = z - 1

x = 4 + y - z

x + y - 3z = -2

A. {(3, -1, 0)}

B. {(2, -1, 0)}

C. {(3, -2, 1)}

D. {(2, -1, 1)}

Question 19 of 40

2.5/ 2.5 Points

Use Cramer’s Rule to solve the following system.

x + 2y + 2z = 5

2x + 4y + 7z = 19

-2x - 5y - 2z = 8

A. {(33, -11, 4)}

B. {(13, 12, -3)}

C. {(23, -12, 3)}

D. {(13, -14, 3)}

Question 20 of 40

Use Cramer’s Rule to solve the following system.

4x - 5y = 17

2x + 3y = 3

A. {(3, -1)}

B. {(2, -1)}

C. {(3, -7)}

D. {(2, 0)}

Part 2 of 2 - Lesson 7 Questions 20.0/ 50.0 Points

Question 21 of 40

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 1)2 = -8x

A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2

B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3

C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1

D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5

Question 22 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1

B. (x - 1)2/18 + (y + 2)2/71 = 1

C. (x - 1)2/16 + (y + 2)2/9 = 1

D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 23 of 40

2.5/ 2.5 Points

Find the focus and directrix of the parabola with the given equation.

8x2 + 4y = 0

A. Focus: (0, -1/4); directrix: y = 1/4

B. Focus: (0, -1/6); directrix: y = 1/6

C. Focus: (0, -1/8); directrix: y = 1/8

D. Focus: (0, -1/2); directrix: y = 1/2

Question 24 of 40

Locate the foci and find the equations of the asymptotes.

x2/100 - y2/64 = 1

A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x

B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x

C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x

D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x

Question 25 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (0, -3), (0, 3)

Vertices: (0, -1), (0, 1)

A. y2 - x2/4 = 0

B. y2 - x2/8 = 1

C. y2 - x2/3 = 1

D. y2 - x2/2 = 0

Question 26 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

x2 - 2x - 4y + 9 = 0

A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1

B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3

C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1

D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5

Question 27 of 40

2.5/ 2.5 Points

Find the vertices and locate the foci of each hyperbola with the given equation.

x2/4 - y2/1 =1

A.

Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)

B.

Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)

C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)

D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)

Question 28 of 40

2.5/ 2.5 Points

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1

B. (x - 2)2/24 + (y + 1)2/36 = 1

C. (x - 2)2/35 + (y + 1)2/25 = 1

D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 29 of 40

Convert each equation to standard form by completing the square on x and y.

4x2 + y2 + 16x - 6y - 39 = 0

A. (x + 2)2/4 + (y - 3)2/39 = 1

B. (x + 2)2/39 + (y - 4)2/64 = 1

C. (x + 2)2/16 + (y - 3)2/64 = 1

D. (x + 2)2/6 + (y - 3)2/4 = 1

Question 30 of 40

2.5/ 2.5 Points

Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 31 of 40

2.5/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x + 1)2 = -8(y + 1)

A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1

B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1

C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1

D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1

Question 32 of 40

Find the vertices and locate the foci of each hyperbola with the given equation.

y2/4 - x2/1 = 1

A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)

B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)

C.

Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)

D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)

Question 33 of 40

2.5/ 2.5 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x - 2)2 = 8(y - 1)

A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1

B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1

C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1

D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1

Question 34 of 40

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)

Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1

B. (x - 7)2/5 + (y - 6)2/6 = 1

C. (x - 7)2/4 + (y - 6)2/9 = 1

D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 35 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (0, -4), (0, 4)

Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 36 of 40

Find the focus and directrix of each parabola with the given equation.

x2 = -4y

A. Focus: (0, -1), directrix: y = 1

B. Focus: (0, -2), directrix: y = 1

C. Focus: (0, -4), directrix: y = 1

D. Focus: (0, -1), directrix: y = 2

Question 37 of 40

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9

B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6

C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6

D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8

Question 38 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-5, 0), (5, 0)

Vertices: (-8, 0), (8, 0)

A. x2/49 + y2/ 25 = 1

B. x2/64 + y2/39 = 1

C. x2/56 + y2/29 = 1

D. x2/36 + y2/27 = 1

Question 39 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-2, 0), (2, 0)

Y-intercepts: -3 and 3

A. x2/23 + y2/6 = 1

B. x2/24 + y2/2 = 1

C. x2/13 + y2/9 = 1

D. x2/28 + y2/19 = 1

Question 40 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Endpoints of transverse axis: (0, -6), (0, 6)

Asymptote: y = 2x

A. y2/6 - x2/9 = 1

B. y2/36 - x2/9 = 1

C. y2/37 - x2/27 = 1

D. y2/9 - x2/6 = 1

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