Question 1

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x  2 + y  2 + Dx + Ey + F = 0. Center at (0, -5)and r = 6

Accepted Answer

A) x  2 + y  2 - 10 y - 61 = 0 
B) x  2 + y  2 - 10 y + 25 = 0 
C) x  2 + y  2 + 10 y - 11 = 0 
D) x  2 + y  2 + 10 y + 25 = 0 
A) x  2 + y  2 - 10 y - 61 = 0 
B) x  2 + y  2 - 10 y + 25 = 0 
C) x  2 + y  2 + 10 y - 11 = 0 
D) x  2 + y  2 + 10 y + 25 = 0 C

Question 2

Graph the equation. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 3

Graph the hyperbola. x  2 + 4 x - 4 y  2 + 32 y - 64 = 0

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    D

Question 4

Graph the equation. $( x - 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 9$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Graph the equation. $$36 x ^ { 2 } - y ^ { 2 } = 36$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Select the graph of the ellipse. $$16 x ^ { 2 } - 96 x + 5 y ^ { 2 } + 10 y + 69 = 0$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Graph $y ^ { 2 } - 16 x ^ { 2 } = 4$ .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Select the graph of the ellipse. $7 x ^ { 2 } + 25 y ^ { 2 } = 175$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Select the graph of the ellipse. $$x ^ { 2 } + 6 x + 9 y ^ { 2 } - 54 y + 81 = 0$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Graph $4 x ^ { 2 } + y ^ { 2 } + 2 x - 15 = 0$ .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Find the vertex of the parabola and graph it. $x = - y ^ { 2 } + 3$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Graph the circle. Give the coordinates of the center. $$x ^ { 2 } + y ^ { 2 } - 2 y = 8$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Graph $y = 2 x ^ { 2 } + 3 x - 1$ .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Graph the equation. x  2 + y  2 = 9

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 15

Graph the ellipse $x ^ { 2 } + 9 y ^ { 2 } = 36$ .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Graph $y = - \frac { 3 } { 5 } x ^ { 2 } - x + \frac { 1 } { 5 }$ .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

For the equation $y ^ { 2 } - 4 x ^ { 2 } = 64$ , find the intercepts and the equations of the asymptotes.

Accepted Answer

A) intercepts: (2, 0), (-2, 0)asymptotes: y = -8 x , y = 8 x 
B) intercepts: (8, 0), (-8, 0)asymptotes: y = -2 x , y = 2 x 
C) intercepts: (8, 0), (-8, 0)asymptotes: x = -2 y , x = 2 y 
D) intercepts: (0, 8), (0, -8)asymptotes: x = -2 y , x = 2 y 
E) intercepts: (0, 8), (0, -8)asymptotes: y = -2 x , y = 2 x 
A) intercepts: (2, 0), (-2, 0)asymptotes: y = -8 x , y = 8 x 
B) intercepts: (8, 0), (-8, 0)asymptotes: y = -2 x , y = 2 x 
C) intercepts: (8, 0), (-8, 0)asymptotes: x = -2 y , x = 2 y 
D) intercepts: (0, 8), (0, -8)asymptotes: x = -2 y , x = 2 y 
E) intercepts: (0, 8), (0, -8)asymptotes: y = -2 x , y = 2 x

Question 18

Find the vertex of the parabola and graph it. $$x = \frac { 1 } { 2 } y ^ { 2 } + 4 y$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x  2 + y  2 + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 7, and abscissa of center is -8

Accepted Answer

A) x  2 + y  2 - 16 x - 14 y + 64 = 0 and x  2 + y  2 - 16 x + 14 y + 64 = 0 
B) x  2 + y  2 + 16 x - 14 y + 64 = 0 
C) x  2 + y  2 + 16 x - 14 y + 64 = 0 and x  2 + y  2 + 16 x + 14 y + 64 = 0 
D) x  2 + y  2 + 16 x + 14 y + 64 = 0 
E) x  2 + y  2 - 16 x + 14 y + 64 = 0 
A) x  2 + y  2 - 16 x - 14 y + 64 = 0 and x  2 + y  2 - 16 x + 14 y + 64 = 0 
B) x  2 + y  2 + 16 x - 14 y + 64 = 0 
C) x  2 + y  2 + 16 x - 14 y + 64 = 0 and x  2 + y  2 + 16 x + 14 y + 64 = 0 
D) x  2 + y  2 + 16 x + 14 y + 64 = 0 
E) x  2 + y  2 - 16 x + 14 y + 64 = 0

Question 20

Graph the hyperbola. -16 x  2 + 128 x + 9 y  2 - 72 y - 148 = 0

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Center at (0, -5)and r = 6

Graph the equation. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the hyperbola. x ² + 4 x - 4 y ² + 32 y - 64 = 0

Graph the equation. $( x - 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 9$

Graph the equation. $36 x ^ { 2 } - y ^ { 2 } = 36$

Select the graph of the ellipse. $16 x ^ { 2 } - 96 x + 5 y ^ { 2 } + 10 y + 69 = 0$

Graph $y ^ { 2 } - 16 x ^ { 2 } = 4$ .

Select the graph of the ellipse. $7 x ^ { 2 } + 25 y ^ { 2 } = 175$

Select the graph of the ellipse. $x ^ { 2 } + 6 x + 9 y ^ { 2 } - 54 y + 81 = 0$

Graph $4 x ^ { 2 } + y ^ { 2 } + 2 x - 15 = 0$ .

Find the vertex of the parabola and graph it. $x = - y ^ { 2 } + 3$

Graph the circle. Give the coordinates of the center. $x ^ { 2 } + y ^ { 2 } - 2 y = 8$

Graph $y = 2 x ^ { 2 } + 3 x - 1$ .

Graph the equation. x ²+ y ²= 9

Graph the ellipse $x ^ { 2 } + 9 y ^ { 2 } = 36$ .

Graph $y = - \frac { 3 } { 5 } x ^ { 2 } - x + \frac { 1 } { 5 }$ .

For the equation $y ^ { 2 } - 4 x ^ { 2 } = 64$ , find the intercepts and the equations of the asymptotes.

Find the vertex of the parabola and graph it. $x = \frac { 1 } { 2 } y ^ { 2 } + 4 y$

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 7, and abscissa of center is -8

Graph the hyperbola. -16 x ² + 128 x + 9 y ² - 72 y - 148 = 0

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Exam 8: Conic Sections

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x 2 + y 2 + Dx + Ey + F = 0. Center at (0, -5)and r = 6

Graph the equation. x24−y29=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 14x2​−9y2​=1

Graph the hyperbola. x 2 + 4 x - 4 y 2 + 32 y - 64 = 0

Graph the equation. (x−2)2+(y−3)2=9( x - 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 9(x−2)2+(y−3)2=9

Graph the equation. 36x2−y2=3636 x ^ { 2 } - y ^ { 2 } = 3636x2−y2=36

Select the graph of the ellipse. 16x2−96x+5y2+10y+69=016 x ^ { 2 } - 96 x + 5 y ^ { 2 } + 10 y + 69 = 016x2−96x+5y2+10y+69=0

Graph y2−16x2=4y ^ { 2 } - 16 x ^ { 2 } = 4y2−16x2=4 .

Select the graph of the ellipse. 7x2+25y2=1757 x ^ { 2 } + 25 y ^ { 2 } = 1757x2+25y2=175

Select the graph of the ellipse. x2+6x+9y2−54y+81=0x ^ { 2 } + 6 x + 9 y ^ { 2 } - 54 y + 81 = 0x2+6x+9y2−54y+81=0

Graph 4x2+y2+2x−15=04 x ^ { 2 } + y ^ { 2 } + 2 x - 15 = 04x2+y2+2x−15=0 .

Find the vertex of the parabola and graph it. x=−y2+3x = - y ^ { 2 } + 3x=−y2+3

Graph the circle. Give the coordinates of the center. x2+y2−2y=8x ^ { 2 } + y ^ { 2 } - 2 y = 8x2+y2−2y=8

Graph y=2x2+3x−1y = 2 x ^ { 2 } + 3 x - 1y=2x2+3x−1 .

Graph the equation. x 2 + y 2 = 9

Graph the ellipse x2+9y2=36x ^ { 2 } + 9 y ^ { 2 } = 36x2+9y2=36 .

Graph y=−35x2−x+15y = - \frac { 3 } { 5 } x ^ { 2 } - x + \frac { 1 } { 5 }y=−53​x2−x+51​ .

For the equation y2−4x2=64y ^ { 2 } - 4 x ^ { 2 } = 64y2−4x2=64 , find the intercepts and the equations of the asymptotes.

Find the vertex of the parabola and graph it. x=12y2+4yx = \frac { 1 } { 2 } y ^ { 2 } + 4 yx=21​y2+4y

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x 2 + y 2 + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 7, and abscissa of center is -8

Graph the hyperbola. -16 x 2 + 128 x + 9 y 2 - 72 y - 148 = 0

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Functions

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Exponential and Logarithmic Functions

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Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Center at (0, -5)and r = 6

Graph the equation. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the hyperbola. x ² + 4 x - 4 y ² + 32 y - 64 = 0

Graph the equation. $( x - 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 9$

Graph the equation. $36 x ^ { 2 } - y ^ { 2 } = 36$

Select the graph of the ellipse. $16 x ^ { 2 } - 96 x + 5 y ^ { 2 } + 10 y + 69 = 0$

Graph $y ^ { 2 } - 16 x ^ { 2 } = 4$ .

Select the graph of the ellipse. $7 x ^ { 2 } + 25 y ^ { 2 } = 175$

Select the graph of the ellipse. $x ^ { 2 } + 6 x + 9 y ^ { 2 } - 54 y + 81 = 0$

Graph $4 x ^ { 2 } + y ^ { 2 } + 2 x - 15 = 0$ .

Find the vertex of the parabola and graph it. $x = - y ^ { 2 } + 3$

Graph the circle. Give the coordinates of the center. $x ^ { 2 } + y ^ { 2 } - 2 y = 8$

Graph $y = 2 x ^ { 2 } + 3 x - 1$ .

Graph the equation. x ²+ y ²= 9

Graph the ellipse $x ^ { 2 } + 9 y ^ { 2 } = 36$ .

Graph $y = - \frac { 3 } { 5 } x ^ { 2 } - x + \frac { 1 } { 5 }$ .

For the equation $y ^ { 2 } - 4 x ^ { 2 } = 64$ , find the intercepts and the equations of the asymptotes.

Find the vertex of the parabola and graph it. $x = \frac { 1 } { 2 } y ^ { 2 } + 4 y$

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 7, and abscissa of center is -8

Graph the hyperbola. -16 x ² + 128 x + 9 y ² - 72 y - 148 = 0