Which set of parametric equations represents the following line or conic? Use $x = h + a \sec \theta$ and $y = k + b \tan \theta$. $\begin{array} { l l l } \text { Hyperbola: } & \text { vertices } & ( - 10 , - 1 ) , ( 2 , - 1 ) \\ & \text { foci } & ( - 11 , - 1 ) , ( 3 , - 1 ) \end{array}$

A) $x = 4 + \sqrt { 13 } \sec \theta$ $y = 1 + 6 \tan \theta$ B) $x = - 4 + \sqrt { 13 } \sec \theta$ $y = - 1 + 6 \tan \theta$ C) $x = - 1 + \sqrt { 13 } \sec \theta$ $y = - 4 + 6 \tan \theta$ $x = - 4 + 6 \sec \theta$ D) $y = - 1 + \sqrt { 13 } \tan \theta$ $x = - 1 + 6 \sec \theta$ E) $y = - 4 + \sqrt { 13 } \tan \theta$ A) $x = 4 + \sqrt { 13 } \sec \theta$ $y = 1 + 6 \tan \theta$ B) $x = - 4 + \sqrt { 13 } \sec \theta$ $y = - 1 + 6 \tan \theta$ C) $x = - 1 + \sqrt { 13 } \sec \theta$ $y = - 4 + 6 \tan \theta$ $x = - 4 + 6 \sec \theta$ D) $y = - 1 + \sqrt { 13 } \tan \theta$ $x = - 1 + 6 \sec \theta$ E) $y = - 4 + \sqrt { 13 } \tan \theta$

Exam 9: Topics in Analytic Geometry

Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote. Name of Graph Polar Equation Asymptote Hyperbolic Spiral r=- y=-5 Use either grid below for your graph, whichever is more convenient. $Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote. \begin{array}{ccc} \text { Name of Graph } & \text { Polar Equation } & \text { Asymptote } \\ \text { Hyperbolic Spiral } & r=-\frac{5}{\theta} & y=-5 \end{array} Use either grid below for your graph, whichever is more convenient.$ $Use a graphing utility to graph the polar equation and show that the indicated line is an asymptote. \begin{array}{ccc} \text { Name of Graph } & \text { Polar Equation } & \text { Asymptote } \\ \text { Hyperbolic Spiral } & r=-\frac{5}{\theta} & y=-5 \end{array} Use either grid below for your graph, whichever is more convenient.$

(Essay)

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Question 61

Convert the following polar equation to rectangular form. $\theta = \frac { 2 \pi } { 3 }$

(Multiple Choice)

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Question 62

Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ? $y = x ^ { 2 } + 2$

(Multiple Choice)

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Question 63

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

(Multiple Choice)

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Question 64

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 17 x ^ { 2 } + y - 103 = 0$

(Multiple Choice)

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Question 65

Find the standard form of the parabola with the given characteristics. focus: $( 8,13 ) \quad$ directrix: $y = - 1$

(Multiple Choice)

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Question 66

Find the standard form of the equation of the ellipse with the given characteristics. center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

(Multiple Choice)

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Question 67

Find the graph of the following polar equation. $r = - 3 \sin ( 3 \theta )$

(Multiple Choice)

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Question 68

Which answer is a rectangular form of the given polar equation? $r = 10 \cos \theta$

(Multiple Choice)

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Question 69

Which answer is a polar form of the given rectangular equation? $25 x y = 225$

(Multiple Choice)

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Question 70

Find two sets of polar coordinates with $0 \leq \theta < 2 \pi$ for the point $( - 2,0 )$ , given in rectangular coordinates.

(Multiple Choice)

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Question 71

Consider the parametric equations $x = 5 \sqrt { t }$ and $y = 2 + 7 t$ . Find the rectangular equation by eliminating the parameter.

(Multiple Choice)

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Question 72

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form. $113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$

(Multiple Choice)

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Question 73

Find the center and foci of the ellipse. $\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$

(Multiple Choice)

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Question 74

Sketch the graph of the ellipse, using the latera recta. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$ $Sketch the graph of the ellipse, using the latera recta. 4 x ^ { 2 } + 9 y ^ { 2 } = 36$

(Essay)

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Question 75

A projectile is launched from ground level at an angle of $\theta$ with the horizontal. The initial velocity is $v _ { 0 }$ feet per second and the path of the projectile is modeled by the parametric equations $x = \left( v _ { 0 } \cos \theta \right) t$ and $y = \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . Use a graphing utility to graph the paths of a projectile launched from ground level with the values given for $\theta$ and $v _ { 0 }$ . Use the graph to approximate the maximum height and range of the projectile to the nearest foot. $\theta = 55 ^ { \circ } , \quad v _ { 0 } = 56$ feet per second

(Multiple Choice)

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Question 76

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$

(Multiple Choice)

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Question 77

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 (-10,-1),(2,-1) foci (-11,-1),(3,-1)

(Multiple Choice)

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Question 78

Find the graph of the following polar equation. $r = - 3 \cos ( 3 \theta )$

(Multiple Choice)

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Question 79

Find the center and foci of the hyperbola. $\frac { ( y + 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 24 } = 1$

(Multiple Choice)

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Question 80

Showing 61 - 80 of 120

Convert the following polar equation to rectangular form. $\theta = \frac { 2 \pi } { 3 }$

Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ? $y = x ^ { 2 } + 2$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 17 x ^ { 2 } + y - 103 = 0$

Find the standard form of the parabola with the given characteristics. focus: $( 8,13 ) \quad$ directrix: $y = - 1$

Find the standard form of the equation of the ellipse with the given characteristics. center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

Find the graph of the following polar equation. $r = - 3 \sin ( 3 \theta )$

Which answer is a rectangular form of the given polar equation? $r = 10 \cos \theta$

Which answer is a polar form of the given rectangular equation? $25 x y = 225$

Find two sets of polar coordinates with $0 \leq \theta < 2 \pi$ for the point $( - 2,0 )$ , given in rectangular coordinates.

Consider the parametric equations $x = 5 \sqrt { t }$ and $y = 2 + 7 t$ . Find the rectangular equation by eliminating the parameter.

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form. $113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$

Sketch the graph of the ellipse, using the latera recta. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$ $Sketch the graph of the ellipse, using the latera recta. 4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$

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 (-10,-1),(2,-1) foci (-11,-1),(3,-1)

Find the graph of the following polar equation. $r = - 3 \cos ( 3 \theta )$

Find the center and foci of the hyperbola. $\frac { ( y + 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 24 } = 1$

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 a graphing utility to graph the polar equation and show that the indicated line is an asymptote. Name of Graph Polar Equation Asymptote Hyperbolic Spiral r=- y=-5 Use either grid below for your graph, whichever is more convenient.

Convert the following polar equation to rectangular form. θ=2π3\theta = \frac { 2 \pi } { 3 }θ=32π​

Which set of parametric equations represents the graph of the following rectangular equation using t=6−xt = 6 - xt=6−x ? y=x2+2y = x ^ { 2 } + 2y=x2+2

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (−6,−8),(−6,6)( - 6 , - 8 ) , ( - 6,6 ) \quad(−6,−8),(−6,6) minor axis of length: 10

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. 3y2+17x2+y−103=03 y ^ { 2 } + 17 x ^ { 2 } + y - 103 = 03y2+17x2+y−103=0

Find the standard form of the parabola with the given characteristics. focus: (8,13)( 8,13 ) \quad(8,13) directrix: y=−1y = - 1y=−1

Find the standard form of the equation of the ellipse with the given characteristics. center: (−8,−5)a=5c( - 8 , - 5 ) \quad a = 5 c \quad(−8,−5)a=5c foci: (−11,−5),(−5,−5)( - 11 , - 5 ) , ( - 5 , - 5 )(−11,−5),(−5,−5)

Find the graph of the following polar equation. r=−3sin⁡(3θ)r = - 3 \sin ( 3 \theta )r=−3sin(3θ)

Which answer is a rectangular form of the given polar equation? r=10cos⁡θr = 10 \cos \thetar=10cosθ

Which answer is a polar form of the given rectangular equation? 25xy=22525 x y = 22525xy=225

Find two sets of polar coordinates with 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π for the point (−2,0)( - 2,0 )(−2,0) , given in rectangular coordinates.

Consider the parametric equations x=5tx = 5 \sqrt { t }x=5t​ and y=2+7ty = 2 + 7 ty=2+7t . Find the rectangular equation by eliminating the parameter.

Rotate the axes to eliminate the xyx yxy -term in the equation. Then write the equation in standard form. 113x2−30xy+113y2−6272=0113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0113x2−30xy+113y2−6272=0

Find the center and foci of the ellipse. (x−9)232+(y+5)236=1\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 132(x−9)2​+36(y+5)2​=1

Sketch the graph of the ellipse, using the latera recta. 4x2+9y2=364 x ^ { 2 } + 9 y ^ { 2 } = 364x2+9y2=36

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 4x2−3y2−5x+7y+1=04 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 04x2−3y2−5x+7y+1=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 (-10,-1),(2,-1) foci (-11,-1),(3,-1)

Find the graph of the following polar equation. r=−3cos⁡(3θ)r = - 3 \cos ( 3 \theta )r=−3cos(3θ)

Find the center and foci of the hyperbola. (y+1)225−(x+2)224=1\frac { ( y + 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 24 } = 125(y+1)2​−24(x+2)2​=1

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

Convert the following polar equation to rectangular form. $\theta = \frac { 2 \pi } { 3 }$

Which set of parametric equations represents the graph of the following rectangular equation using $t = 6 - x$ ? $y = x ^ { 2 } + 2$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10

Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 17 x ^ { 2 } + y - 103 = 0$

Find the standard form of the parabola with the given characteristics. focus: $( 8,13 ) \quad$ directrix: $y = - 1$

Find the standard form of the equation of the ellipse with the given characteristics. center: $( - 8 , - 5 ) \quad a = 5 c \quad$ foci: $( - 11 , - 5 ) , ( - 5 , - 5 )$

Find the graph of the following polar equation. $r = - 3 \sin ( 3 \theta )$

Which answer is a rectangular form of the given polar equation? $r = 10 \cos \theta$

Which answer is a polar form of the given rectangular equation? $25 x y = 225$

Find two sets of polar coordinates with $0 \leq \theta < 2 \pi$ for the point $( - 2,0 )$ , given in rectangular coordinates.

Consider the parametric equations $x = 5 \sqrt { t }$ and $y = 2 + 7 t$ . Find the rectangular equation by eliminating the parameter.

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form. $113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 9 ) ^ { 2 } } { 32 } + \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$

Sketch the graph of the ellipse, using the latera recta. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$ $Sketch the graph of the ellipse, using the latera recta. 4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $4 x ^ { 2 } - 3 y ^ { 2 } - 5 x + 7 y + 1 = 0$

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 (-10,-1),(2,-1) foci (-11,-1),(3,-1)

Find the graph of the following polar equation. $r = - 3 \cos ( 3 \theta )$

Find the center and foci of the hyperbola. $\frac { ( y + 1 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 24 } = 1$