Exam 10: Conics

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { r } 3 x - y = 21 \\x ^ { 2 } - y ^ { 2 } = 49\end{array} \right.$

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Question 1

Correct Answer:

Verified

B

Identify the center and vertices of the hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 6 ) ^ { 2 } } { 1 } = 1$

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Question 2

Correct Answer:

Verified

A

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( - 2,0 ) , ( 2,0 )$ Asymptotes: $y = 5 x , y = - 5 x$

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Question 3

Correct Answer:

Verified

B

Graph the equation $( x + 2 ) ^ { 2 } = - 3 ( y - 1 )$ .

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Question 4

Identify the vertices and co-vertices of the ellipse $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$ .

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Question 5

Write the standard form of the equation of the parabola with focus (4,5) and its vertex at (9,5).

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Question 6

Graph the hyperbola. $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

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Question 7

Solve the system by the method of substitution. $\left\{ \begin{aligned}y & = x ^ { 2 } - 2 \\7 x + 2 y & = - 4\end{aligned} \right.$

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Question 8

Write the standard form of the equation of the ellipse.

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Question 9

Identify the center and radius of the circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$ .

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Question 10

Identify the vertex and focus of the parabola $y ^ { 2 } = - 7 x$ .

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Question 11

Write the standard form of the equation of the ellipse centered at the origin, having a vertical 20 units and a minor axis of 10 units.

(Multiple Choice)

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Question 12

Write the standard form of the equation of the ellipse centered at the origin. Vertices: $( - 6,0 ) ( 6,0 )$ Co-vertices: $( 0 , - 4 ) , ( 0,4 )$

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Question 13

Solve the system by the method of elimination. $\left\{ \begin{array} { l } 3 x ^ { 2 } + 4 y ^ { 2 } = 59 \\2 x ^ { 2 } + 5 y ^ { 2 } = 72\end{array} \right.$

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Question 14

Use a graphing calculator to graph the equations $\left\{ \begin{array} { c } x - 4 y = 1 \\\sqrt { x } - 1 = y\end{array} \right.$ and find the solutions of the system.

(Multiple Choice)

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Question 15

Identify the vertices and center of the ellipse. $25 ( x - 2 ) ^ { 2 } + 9 ( y + 6 ) ^ { 2 } = 4$

(Multiple Choice)

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Question 16

Identify the vertices and center of the ellipse. $25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$

(Multiple Choice)

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Question 17

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { c } 9 x ^ { 2 } - 4 y ^ { 2 } = 36 \\8 x - 2 y = 0\end{array} \right.$

(Multiple Choice)

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Question 18

Graph the hyperbola. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$

(Multiple Choice)

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Question 19

Solve the system by the method of substitution. $\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = 42\end{array} \right.$

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Question 20

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { r } 3 x - y = 21 \\x ^ { 2 } - y ^ { 2 } = 49\end{array} \right.$

Identify the center and vertices of the hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 6 ) ^ { 2 } } { 1 } = 1$

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( - 2,0 ) , ( 2,0 )$ Asymptotes: $y = 5 x , y = - 5 x$

Graph the equation $( x + 2 ) ^ { 2 } = - 3 ( y - 1 )$ .

Identify the vertices and co-vertices of the ellipse $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$ .

Write the standard form of the equation of the parabola with focus (4,5) and its vertex at (9,5).

Graph the hyperbola. $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Solve the system by the method of substitution. $\left\{ \begin{aligned}y & = x ^ { 2 } - 2 \\7 x + 2 y & = - 4\end{aligned} \right.$

Write the standard form of the equation of the ellipse.

Identify the center and radius of the circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$ .

Identify the vertex and focus of the parabola $y ^ { 2 } = - 7 x$ .

Write the standard form of the equation of the ellipse centered at the origin, having a vertical 20 units and a minor axis of 10 units.

Write the standard form of the equation of the ellipse centered at the origin. Vertices: $( - 6,0 ) ( 6,0 )$ Co-vertices: $( 0 , - 4 ) , ( 0,4 )$

Solve the system by the method of elimination. $\left\{ \begin{array} { l } 3 x ^ { 2 } + 4 y ^ { 2 } = 59 \\2 x ^ { 2 } + 5 y ^ { 2 } = 72\end{array} \right.$

Use a graphing calculator to graph the equations $\left\{ \begin{array} { c } x - 4 y = 1 \\\sqrt { x } - 1 = y\end{array} \right.$ and find the solutions of the system.

Identify the vertices and center of the ellipse. $25 ( x - 2 ) ^ { 2 } + 9 ( y + 6 ) ^ { 2 } = 4$

Identify the vertices and center of the ellipse. $25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { c } 9 x ^ { 2 } - 4 y ^ { 2 } = 36 \\8 x - 2 y = 0\end{array} \right.$

Graph the hyperbola. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = 42\end{array} \right.$

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Exam 10: Conics

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. {3x−y=21x2−y2=49\left\{ \begin{array} { r } 3 x - y = 21 \\x ^ { 2 } - y ^ { 2 } = 49\end{array} \right.{3x−y=21x2−y2=49​

Identify the center and vertices of the hyperbola. (x−2)225−(y+6)21=1\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 6 ) ^ { 2 } } { 1 } = 125(x−2)2​−1(y+6)2​=1

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: (−2,0),(2,0)( - 2,0 ) , ( 2,0 )(−2,0),(2,0) Asymptotes: y=5x,y=−5xy = 5 x , y = - 5 xy=5x,y=−5x

Graph the equation (x+2)2=−3(y−1)( x + 2 ) ^ { 2 } = - 3 ( y - 1 )(x+2)2=−3(y−1) .

Identify the vertices and co-vertices of the ellipse x249+y24=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 149x2​+4y2​=1 .

Write the standard form of the equation of the parabola with focus (4,5) and its vertex at (9,5).

Graph the hyperbola. y29−x236=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 19y2​−36x2​=1

Solve the system by the method of substitution. {y=x2−27x+2y=−4\left\{ \begin{aligned}y & = x ^ { 2 } - 2 \\7 x + 2 y & = - 4\end{aligned} \right.{y7x+2y​=x2−2=−4​

Write the standard form of the equation of the ellipse.

Identify the center and radius of the circle 9x2+9y2−16=09 x ^ { 2 } + 9 y ^ { 2 } - 16 = 09x2+9y2−16=0 .

Identify the vertex and focus of the parabola y2=−7xy ^ { 2 } = - 7 xy2=−7x .

Write the standard form of the equation of the ellipse centered at the origin, having a vertical 20 units and a minor axis of 10 units.

Write the standard form of the equation of the ellipse centered at the origin. Vertices: (−6,0)(6,0)( - 6,0 ) ( 6,0 )(−6,0)(6,0) Co-vertices: (0,−4),(0,4)( 0 , - 4 ) , ( 0,4 )(0,−4),(0,4)

Solve the system by the method of elimination. {3x2+4y2=592x2+5y2=72\left\{ \begin{array} { l } 3 x ^ { 2 } + 4 y ^ { 2 } = 59 \\2 x ^ { 2 } + 5 y ^ { 2 } = 72\end{array} \right.{3x2+4y2=592x2+5y2=72​

Use a graphing calculator to graph the equations {x−4y=1x−1=y\left\{ \begin{array} { c } x - 4 y = 1 \\\sqrt { x } - 1 = y\end{array} \right.{x−4y=1x​−1=y​ and find the solutions of the system.

Identify the vertices and center of the ellipse. 25(x−2)2+9(y+6)2=425 ( x - 2 ) ^ { 2 } + 9 ( y + 6 ) ^ { 2 } = 425(x−2)2+9(y+6)2=4

Identify the vertices and center of the ellipse. 25x2+16y2−100x+96y−156=025 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 025x2+16y2−100x+96y−156=0

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. {9x2−4y2=368x−2y=0\left\{ \begin{array} { c } 9 x ^ { 2 } - 4 y ^ { 2 } = 36 \\8 x - 2 y = 0\end{array} \right.{9x2−4y2=368x−2y=0​

Graph the hyperbola. x29−y236=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 19x2​−36y2​=1

Solve the system by the method of substitution. {x−y2=0x−y=42\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = 42\end{array} \right.{x−y2=0x−y=42​

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

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Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { r } 3 x - y = 21 \\x ^ { 2 } - y ^ { 2 } = 49\end{array} \right.$

Identify the center and vertices of the hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 6 ) ^ { 2 } } { 1 } = 1$

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( - 2,0 ) , ( 2,0 )$ Asymptotes: $y = 5 x , y = - 5 x$

Graph the equation $( x + 2 ) ^ { 2 } = - 3 ( y - 1 )$ .

Identify the vertices and co-vertices of the ellipse $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$ .

Graph the hyperbola. $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Solve the system by the method of substitution. $\left\{ \begin{aligned}y & = x ^ { 2 } - 2 \\7 x + 2 y & = - 4\end{aligned} \right.$

Identify the center and radius of the circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$ .

Identify the vertex and focus of the parabola $y ^ { 2 } = - 7 x$ .

Write the standard form of the equation of the ellipse centered at the origin. Vertices: $( - 6,0 ) ( 6,0 )$ Co-vertices: $( 0 , - 4 ) , ( 0,4 )$

Solve the system by the method of elimination. $\left\{ \begin{array} { l } 3 x ^ { 2 } + 4 y ^ { 2 } = 59 \\2 x ^ { 2 } + 5 y ^ { 2 } = 72\end{array} \right.$

Use a graphing calculator to graph the equations $\left\{ \begin{array} { c } x - 4 y = 1 \\\sqrt { x } - 1 = y\end{array} \right.$ and find the solutions of the system.

Identify the vertices and center of the ellipse. $25 ( x - 2 ) ^ { 2 } + 9 ( y + 6 ) ^ { 2 } = 4$

Identify the vertices and center of the ellipse. $25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $\left\{ \begin{array} { c } 9 x ^ { 2 } - 4 y ^ { 2 } = 36 \\8 x - 2 y = 0\end{array} \right.$

Graph the hyperbola. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = 42\end{array} \right.$