Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$. $\begin{array} { l l l } \text { Hyperbola: } & \text { vertices } & ( - 5,7 ) , ( - 3,7 ) \\ & \text { foci } & ( - 8,7 ) , ( 0,7 ) \end{array}$

A) \[\begin{array} { l } x = 4 + \sqrt { 15 } \sec \theta \\ y = - 7 + \tan \theta \end{array}\] B) \[\begin{array} { l } x = - 4 + \sqrt { 15 } \sec \theta \\ y = 7 + \tan \theta \end{array}\] C) \[\begin{array} { l } x = 7 + \sqrt { 15 } \sec \theta \\ y = - 4 + \tan \theta \\ \end{array}\] D) $x=-4+\sec \theta$ \[y = 7 + \sqrt { 15 } \tan \theta\] E) \[\begin{array} { l } x = 7 + \sec \theta \\ y = - 4 + \sqrt { 15 } \tan \theta \end{array}\] A) \[\begin{array} { l } x = 4 + \sqrt { 15 } \sec \theta \\ y = - 7 + \tan \theta \end{array}\] B) \[\begin{array} { l } x = - 4 + \sqrt { 15 } \sec \theta \\ y = 7 + \tan \theta \end{array}\] C) \[\begin{array} { l } x = 7 + \sqrt { 15 } \sec \theta \\ y = - 4 + \tan \theta \\ \end{array}\] D) $x=-4+\sec \theta$ \[y = 7 + \sqrt { 15 } \tan \theta\] E) \[\begin{array} { l } x = 7 + \sec \theta \\ y = - 4 + \sqrt { 15 } \tan \theta \end{array}\]

Exam 9: Topics in Analytic Geometry

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ . $3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 0$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

C

Find the vertex and focus of the parabola. $x ^ { 2 } - 8 y = 0$

Free

(Multiple Choice)

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(26)

Question 2

Correct Answer:

Verified

D

Match the graph with its equation

Free

(Multiple Choice)

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(29)

Question 3

Correct Answer:

Verified

B

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( 4 , - 6 ) , ( 4,10 ) \quad$ minor axis of length: 4

(Multiple Choice)

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Question 4

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 3 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

(Multiple Choice)

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(40)

Question 5

Find the standard form of the parabola with the given characteristics.

(Multiple Choice)

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Question 6

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 2 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

(Multiple Choice)

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Question 7

Find the $y$ -intercepts of the graph of the circle below. $( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$

(Multiple Choice)

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Question 8

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 5,0 )$ asymptotes: $y = \pm 3 x$

(Multiple Choice)

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Question 9

Match the graph with its equation.

(Multiple Choice)

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Question 10

Sketch the curve represented by the following parametric equations. Indicate the orientation of the curve. $x = e ^ { t } , y = e ^ { - 2 t }$

(Multiple Choice)

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Question 11

Find the vertex and focus of the parabola below. $y ^ { 2 } + 10 y - 8 x + 30 = 0$

(Multiple Choice)

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Question 12

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices (-5,7),(-3,7) foci (-8,7),(0,7)

(Multiple Choice)

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Question 13

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$ , the polar axis, and the pole. $r = 2 - 2 \sin ( 4 \theta )$

(Multiple Choice)

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Question 14

Which answer is a rectangular form of the given polar equation? $r = \frac { 5 } { 8 + \sin \theta }$

(Multiple Choice)

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Question 15

Use a graphing utility to graph the polar equation. Describe the resulting graph. $r = 4 \cos ( 7 \theta - 2 )$

(Multiple Choice)

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Question 16

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $7 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 0$

(Multiple Choice)

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Question 17

Find the standard form of the parabola with the given characteristic and vertex at the origin. vertical axis and passes through point $( 10 , - 10 )$

(Multiple Choice)

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Question 18

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 19 x ^ { 2 } + y - 115 = 0$

(Multiple Choice)

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Question 19

Find the standard form of the equation of the following hyperbola. $10 x ^ { 2 } - 6 y ^ { 2 } = 60$

(Multiple Choice)

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Question 20

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ . $3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 0$

Find the vertex and focus of the parabola. $x ^ { 2 } - 8 y = 0$

Match the graph with its equation

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( 4 , - 6 ) , ( 4,10 ) \quad$ minor axis of length: 4

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 3 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

Find the standard form of the parabola with the given characteristics.

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 2 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

Find the $y$ -intercepts of the graph of the circle below. $( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 5,0 )$ asymptotes: $y = \pm 3 x$

Match the graph with its equation.

Sketch the curve represented by the following parametric equations. Indicate the orientation of the curve. $x = e ^ { t } , y = e ^ { - 2 t }$

Find the vertex and focus of the parabola below. $y ^ { 2 } + 10 y - 8 x + 30 = 0$

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices (-5,7),(-3,7) foci (-8,7),(0,7)

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$ , the polar axis, and the pole. $r = 2 - 2 \sin ( 4 \theta )$

Which answer is a rectangular form of the given polar equation? $r = \frac { 5 } { 8 + \sin \theta }$

Use a graphing utility to graph the polar equation. Describe the resulting graph. $r = 4 \cos ( 7 \theta - 2 )$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $7 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 0$

Find the standard form of the parabola with the given characteristic and vertex at the origin. vertical axis and passes through point $( 10 , - 10 )$

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 19 x ^ { 2 } + y - 115 = 0$

Find the standard form of the equation of the following hyperbola. $10 x ^ { 2 } - 6 y ^ { 2 } = 60$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 9: Topics in Analytic Geometry

Use the discriminant to classify the graph; then use the quadratic formula to solve for yyy . 3x2−23xy+y2−183x+30y+36=03 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 03x2−23​xy+y2−183​x+30y+36=0

Find the vertex and focus of the parabola. x2−8y=0x ^ { 2 } - 8 y = 0x2−8y=0

Match the graph with its equation

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (4,−6),(4,10)( 4 , - 6 ) , ( 4,10 ) \quad(4,−6),(4,10) minor axis of length: 4

Find three additional polar representations of the point (5,−π3)\left( 5 , - \frac { \pi } { 3 } \right)(5,−3π​) , given in polar coordinates, using −2π<θ<2π- 2 \pi < \theta < 2 \pi−2π<θ<2π .

Find the standard form of the parabola with the given characteristics.

Find three additional polar representations of the point (5,−π2)\left( 5 , - \frac { \pi } { 2 } \right)(5,−2π​) , given in polar coordinates, using −2π<θ<2π- 2 \pi < \theta < 2 \pi−2π<θ<2π .

Find the yyy -intercepts of the graph of the circle below. (x−5)2+(y+2)2=36( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36(x−5)2+(y+2)2=36

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±5,0)( \pm 5,0 )(±5,0) asymptotes: y=±3xy = \pm 3 xy=±3x

Match the graph with its equation.

Sketch the curve represented by the following parametric equations. Indicate the orientation of the curve. x=et,y=e−2tx = e ^ { t } , y = e ^ { - 2 t }x=et,y=e−2t

Find the vertex and focus of the parabola below. y2+10y−8x+30=0y ^ { 2 } + 10 y - 8 x + 30 = 0y2+10y−8x+30=0

Which set of parametric equations represents the following line or conic? Use x=h+asec⁡θx = h + a \sec \thetax=h+asecθ and y=k+btan⁡θy = k + b \tan \thetay=k+btanθ . Hyperbola: vertices (-5,7),(-3,7) foci (-8,7),(0,7)

Test the graph of the following equation for symmetry with respect to θ=π2\theta = \frac { \pi } { 2 }θ=2π​ , the polar axis, and the pole. r=2−2sin⁡(4θ)r = 2 - 2 \sin ( 4 \theta )r=2−2sin(4θ)

Which answer is a rectangular form of the given polar equation? r=58+sin⁡θr = \frac { 5 } { 8 + \sin \theta }r=8+sinθ5​

Use a graphing utility to graph the polar equation. Describe the resulting graph. r=4cos⁡(7θ−2)r = 4 \cos ( 7 \theta - 2 )r=4cos(7θ−2)

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 7x2+7y2−7x+9y−2=07 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 07x2+7y2−7x+9y−2=0

Find the standard form of the parabola with the given characteristic and vertex at the origin. vertical axis and passes through point (10,−10)( 10 , - 10 )(10,−10)

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. 3y2+19x2+y−115=03 y ^ { 2 } + 19 x ^ { 2 } + y - 115 = 03y2+19x2+y−115=0

Find the standard form of the equation of the following hyperbola. 10x2−6y2=6010 x ^ { 2 } - 6 y ^ { 2 } = 6010x2−6y2=60

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ . $3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 0$

Find the vertex and focus of the parabola. $x ^ { 2 } - 8 y = 0$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( 4 , - 6 ) , ( 4,10 ) \quad$ minor axis of length: 4

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 3 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 2 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

Find the $y$ -intercepts of the graph of the circle below. $( x - 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$

Find the standard form of the equation of the hyperbola with the given characteristics. foci: $( \pm 5,0 )$ asymptotes: $y = \pm 3 x$

Sketch the curve represented by the following parametric equations. Indicate the orientation of the curve. $x = e ^ { t } , y = e ^ { - 2 t }$

Find the vertex and focus of the parabola below. $y ^ { 2 } + 10 y - 8 x + 30 = 0$

Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$ . Hyperbola: vertices (-5,7),(-3,7) foci (-8,7),(0,7)

Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$ , the polar axis, and the pole. $r = 2 - 2 \sin ( 4 \theta )$

Which answer is a rectangular form of the given polar equation? $r = \frac { 5 } { 8 + \sin \theta }$

Use a graphing utility to graph the polar equation. Describe the resulting graph. $r = 4 \cos ( 7 \theta - 2 )$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $7 x ^ { 2 } + 7 y ^ { 2 } - 7 x + 9 y - 2 = 0$

Find the standard form of the parabola with the given characteristic and vertex at the origin. vertical axis and passes through point $( 10 , - 10 )$

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 19 x ^ { 2 } + y - 115 = 0$

Find the standard form of the equation of the following hyperbola. $10 x ^ { 2 } - 6 y ^ { 2 } = 60$