Question 1

Find a polar equation of the conic with its focus at the pole. 
Conics $\quad$$\quad$Eccentricity$\quad$$\quad$ Directrix
Ellipse $\quad\quad\quad e = 1 \quad\quad\quad y = -2$

Accepted Answer

A)  $r = \frac { - 2 } { 1 - \cos \theta }$ 
B)  $r = \frac { 2 } { 1 + \cos \theta }$ 
C)  $r = \frac { 2 } { 1 - \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - \sin \theta }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta }$ 
A)  $r = \frac { - 2 } { 1 - \cos \theta }$ 
B)  $r = \frac { 2 } { 1 + \cos \theta }$ 
C)  $r = \frac { 2 } { 1 - \cos \theta }$ 
D)  $r = \frac { 2 } { 1 - \sin \theta }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta }$

Question 2

Find the standard form of the equation of the parabola with the given characteristics. 
Vertex: $( 0,2 )$ ; directrix: $y = 10$

Accepted Answer

A)  $x ^ { 2 } = - 32 ( y - 10 )$ 
B)  $y ^ { 2 } = - 32 ( x - 2 )$ 
C)  $x ^ { 2 } = 32 ( y - 2 )$ 
D)  $y ^ { 2 } = 32 ( x - 2 )$ 
E)  $x ^ { 2 } = - 32 ( y - 2 )$ 
A)  $x ^ { 2 } = - 32 ( y - 10 )$ 
B)  $y ^ { 2 } = - 32 ( x - 2 )$ 
C)  $x ^ { 2 } = 32 ( y - 2 )$ 
D)  $y ^ { 2 } = 32 ( x - 2 )$ 
E)  $x ^ { 2 } = - 32 ( y - 2 )$

Question 3

Find the center, vertices and foci of the hyperbola.  $26 y ^ { 2 } - 23 x ^ { 2 } = 598$

Accepted Answer

A) Center: (0, 0)Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
B) Center: $( 23,26 )$  Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
C) Center: (0, 0)Vertices: $( \pm \sqrt { 49 } , 0 )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
D) Center: (0, 0)Vertices: $( \pm \sqrt { 7 } , 0 )$ Foci: $( \pm \sqrt { 49 } , 0 )$ 
E) Center: $( 26,23 )$ Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
A) Center: (0, 0)Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
B) Center: $( 23,26 )$  Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
C) Center: (0, 0)Vertices: $( \pm \sqrt { 49 } , 0 )$ Foci: $( 0 , \pm \sqrt { 49 } )$ 
D) Center: (0, 0)Vertices: $( \pm \sqrt { 7 } , 0 )$ Foci: $( \pm \sqrt { 49 } , 0 )$ 
E) Center: $( 26,23 )$ Vertices: $( 0 , \pm \sqrt { 7 } )$ Foci: $( 0 , \pm \sqrt { 49 } )$

Question 4

Find the standard form of the equation of the hyperbola with the given characteristics. 
vertices: (3, 3), (3, 7)
Foci: (3, 1), (3, 9)

Accepted Answer

A)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
B)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } + \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 4 } - \frac { ( y - 3 ) ^ { 2 } } { 12 } = 1$ 
D)  $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
E)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 12 } = 1$ 
A)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
B)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } + \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 4 } - \frac { ( y - 3 ) ^ { 2 } } { 12 } = 1$ 
D)  $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 12 } = 1$ 
E)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 12 } = 1$

Question 5

Using following result find a set of parametric equation of the line.  $x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right) , y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$ 
Line: passes through $( 9,2 )$ and $( - 3,9 )$

Accepted Answer

A)  $x = 9 + 12 t , y = 2 + 7 t$ 
B)  $x = 2 - 12 t , y = 2 + 7 t$ , 
C)  $x = 2 - 12 t , y = 9 - 7 t$ , 
D)  $x = 2 - 12 t , y = 9 + 7 t$ 
E)  $x = 9 - 12 t , y = 2 + 7 t$ 
A)  $x = 9 + 12 t , y = 2 + 7 t$ 
B)  $x = 2 - 12 t , y = 2 + 7 t$ , 
C)  $x = 2 - 12 t , y = 9 - 7 t$ , 
D)  $x = 2 - 12 t , y = 9 + 7 t$ 
E)  $x = 9 - 12 t , y = 2 + 7 t$

Question 6

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Accepted Answer

A)  $x ^ { 2 } = \frac { 2 } { 4 } y$ 
B)  $y ^ { 2 } = \frac { 2 } { 4 } x$ 
C)  $y ^ { 2 } = \frac { 4 } { 2 } x$ 
D)  $x ^ { 2 } = \frac { 4 } { 2 } y$ 
E)  $y ^ { 2 } = x$ 
A)  $x ^ { 2 } = \frac { 2 } { 4 } y$ 
B)  $y ^ { 2 } = \frac { 2 } { 4 } x$ 
C)  $y ^ { 2 } = \frac { 4 } { 2 } x$ 
D)  $x ^ { 2 } = \frac { 4 } { 2 } y$ 
E)  $y ^ { 2 } = x$

Question 7

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line.

Accepted Answer

A)  $m = 3$ 
B)  $m = - 1$ 
C)  $m = 2$ 
D)  $m = - 2$ 
E)  $m = 1$ 
A)  $m = 3$ 
B)  $m = - 1$ 
C)  $m = 2$ 
D)  $m = - 2$ 
E)  $m = 1$

Question 8

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: $( 0 , \pm 6 )$ ; asymptotes: $y = \pm 6 x$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 36 } + \frac { x ^ { 2 } } { 1 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 1 } = 1$ 
D)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 1 } = 1$ 
E)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 1 } = 1$ 
A)  $\frac { y ^ { 2 } } { 1 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 36 } + \frac { x ^ { 2 } } { 1 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 1 } = 1$ 
D)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 1 } = 1$ 
E)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 1 } = 1$

Question 9

Select the graph of the following equation.  $x y + 4 = 0$

Accepted Answer

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

Question 10

Find the distance between the point and the line.Round your answer to four decimal places. Point Line
$( 4,5 ) \quad 7 x + y = 1$

Accepted Answer

A)  $d \approx 4.7068$ 
B)  $d \approx 5.7068$ 
C)  $d \approx 6.7068$ 
D)  $d \approx 3.7068$ 
E)  $d \approx 7.7068$ 
A)  $d \approx 4.7068$ 
B)  $d \approx 5.7068$ 
C)  $d \approx 6.7068$ 
D)  $d \approx 3.7068$ 
E)  $d \approx 7.7068$

Question 11

Sketch the graph of the ellipse, using the latera recta.
 $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

The answer of Sketch the graph of the ellipse, using...

Question 12

Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$

Accepted Answer

A) vertex: $( 6 , - 3 )$ focus: $( 6,5 )$ 
B) vertex: $( 6 , - 3 )$ focus: $( 6 , - 11 )$ 
C) vertex: $( 6 , - 3 )$ focus: $( 4 , - 3 )$ 
D) vertex: $( - 6,3 )$ focus: $( - 8,3 )$ 
E) vertex: $( - 6,3 )$ focus: $( - 6 , - 3 )$ 
A) vertex: $( 6 , - 3 )$ focus: $( 6,5 )$ 
B) vertex: $( 6 , - 3 )$ focus: $( 6 , - 11 )$ 
C) vertex: $( 6 , - 3 )$ focus: $( 4 , - 3 )$ 
D) vertex: $( - 6,3 )$ focus: $( - 8,3 )$ 
E) vertex: $( - 6,3 )$ focus: $( - 6 , - 3 )$

Question 13

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once.  $r ^ { 2 } = 4 \sin 2 \theta$

Accepted Answer

A)   $0 \leq \theta < \pi$ 
B)    $0 \leq \theta < \pi$ 
C)    $0 \leq \theta < \pi$ 
D)   $0 \leq \theta < \pi$ 
E)    $0 \leq \theta < \pi$ 
A)   $0 \leq \theta < \pi$ 
B)    $0 \leq \theta < \pi$ 
C)    $0 \leq \theta < \pi$ 
D)   $0 \leq \theta < \pi$ 
E)    $0 \leq \theta < \pi$

Question 14

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates, r > 0.Round your answers to three decimal places.  $( 3 , - 2 )$

Accepted Answer

A) Polar coordinates: $( \sqrt { 2 } , - 0.588 )$ 
B) Polar coordinates: $( \sqrt { 1 } , - 0.588 )$ 
C) Polar coordinates: $( \sqrt { 13 } , - 0.588 )$ 
D) Polar coordinates: $( \sqrt { 13 } , 0.588 )$ 
E) Polar coordinates: $( \sqrt { 3 } , - 0.588 )$ 
A) Polar coordinates: $( \sqrt { 2 } , - 0.588 )$ 
B) Polar coordinates: $( \sqrt { 1 } , - 0.588 )$ 
C) Polar coordinates: $( \sqrt { 13 } , - 0.588 )$ 
D) Polar coordinates: $( \sqrt { 13 } , 0.588 )$ 
E) Polar coordinates: $( \sqrt { 3 } , - 0.588 )$

Question 15

Identify the conic and select its correct graph.  $r = \frac { 9 } { 1 + \cos \theta }$

Accepted Answer

A)  $e = 1 \Rightarrow$ Parabola   
B)  $e = 1 \Rightarrow$ Parabola   
C)  $e = 2 \Rightarrow$ Hyperbola   
D)  $e = 1 \Rightarrow$ Parabola   
E)  $e = 1 \Rightarrow$ Parabola   
A)  $e = 1 \Rightarrow$ Parabola   
B)  $e = 1 \Rightarrow$ Parabola   
C)  $e = 2 \Rightarrow$ Hyperbola   
D)  $e = 1 \Rightarrow$ Parabola   
E)  $e = 1 \Rightarrow$ Parabola

Question 16

A satellite in a 100-mile-high circular orbit around Earth has a velocity of approximately 17,500 miles per hour.If this velocity is multiplied by $\sqrt { 2 }$ , the satellite will have the minimum velocity necessary to escape Earth's gravity and will follow a parabolic path with the center of Earth as the focus.(Hints: The radius of Earth is 4000 miles.)    Find the distance between the surface of the Earth and the satellite when $\theta = 50 ^ { \circ }$ .

Accepted Answer

A) Distance between surface of Earth and satellite:4496 miles 
B) Distance between surface of Earth and satellite:4322 miles 
C) Distance between surface of Earth and satellite:1286 miles 
D) Distance between surface of Earth and satellite:643 miles 
E) Distance between surface of Earth and satellite:1492 miles 
A) Distance between surface of Earth and satellite:4496 miles 
B) Distance between surface of Earth and satellite:4322 miles 
C) Distance between surface of Earth and satellite:1286 miles 
D) Distance between surface of Earth and satellite:643 miles 
E) Distance between surface of Earth and satellite:1492 miles

Question 17

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 3 } { 4 } x$

Accepted Answer

A) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( - \frac { 3 } { 4 } , - \frac { 3 } { 4 } \right)$ 
B) vertex: (0, 0) focus: $\left( 0 , - \frac { 3 } { 4 } \right)$ 
C) vertex: (0, 0) focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ 
D) vertex: (0, 0) focus: $\left( - \frac { 3 } { 16 } , 0 \right)$ 
E) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( 0 , - \frac { 3 } { 16 } \right)$ 
A) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( - \frac { 3 } { 4 } , - \frac { 3 } { 4 } \right)$ 
B) vertex: (0, 0) focus: $\left( 0 , - \frac { 3 } { 4 } \right)$ 
C) vertex: (0, 0) focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ 
D) vertex: (0, 0) focus: $\left( - \frac { 3 } { 16 } , 0 \right)$ 
E) vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( 0 , - \frac { 3 } { 16 } \right)$

Question 18

Find the vertex and directrix of the parabola. $x ^ { 2 } - 18 x - 12 y + 33 = 0$

Accepted Answer

A) vertex: $( - 9,4 )$ directrix: y=1 
B) vertex: $( - 9,4 )$ directrix: y=12 
C) vertex: $( - 9,4 )$ directrix: y=6 
D) vertex: $( 9 , - 4 )$ directrix: y=-1 
E) vertex: $( 9 , - 4 )$ directrix: y=-7 
A) vertex: $( - 9,4 )$ directrix: y=1 
B) vertex: $( - 9,4 )$ directrix: y=12 
C) vertex: $( - 9,4 )$ directrix: y=6 
D) vertex: $( 9 , - 4 )$ directrix: y=-1 
E) vertex: $( 9 , - 4 )$ directrix: y=-7

Question 19

Convert the rectangular equation to polar form.Assume r > 1. $7 x - y + 6 = 0$

Accepted Answer

A)  $y = \frac { - 6 } { 7 \cos \Theta - 6 \sin \theta }$ 
B)  $y = \frac { - 7 } { 6 \cos \Theta - \sin \Theta }$ 
C)  $y = \frac { - 6 } { 7 \cos \theta + \sin \theta }$ 
D)  $y = \frac { 6 } { 7 \cos \theta - \sin \theta }$ 
E)  $y = \frac { - 6 } { 7 \cos \theta - \sin \theta }$ 
A)  $y = \frac { - 6 } { 7 \cos \Theta - 6 \sin \theta }$ 
B)  $y = \frac { - 7 } { 6 \cos \Theta - \sin \Theta }$ 
C)  $y = \frac { - 6 } { 7 \cos \theta + \sin \theta }$ 
D)  $y = \frac { 6 } { 7 \cos \theta - \sin \theta }$ 
E)  $y = \frac { - 6 } { 7 \cos \theta - \sin \theta }$

Question 20

Find the center, vertices and foci of the hyperbola.  $3 x ^ { 2 } - 4 y ^ { 2 } = 12$

Accepted Answer

A) Center: (1, 1)Vertices: (±4, 0)Foci: $( \pm \sqrt { 7 } , 0 )$ 
B) Center: $( 3,4 )$ Vertices: (±4, 0)Foci: $( \pm \sqrt { 7 } , 0 )$ 
C) Center: (0, 0)Vertices: (0, ± $2$ )Foci: $( 0 , \pm \sqrt { 7 } )$ 
D) Center: (1, 1)Vertices: (0, ± $2$ )Foci: $( 0 , \pm \sqrt { 7 } )$ 
E) Center: (0, 0)Vertices: (± $2$ , 0)Foci: $( \pm \sqrt { 7 } , 0 )$ 
A) Center: (1, 1)Vertices: (±4, 0)Foci: $( \pm \sqrt { 7 } , 0 )$ 
B) Center: $( 3,4 )$ Vertices: (±4, 0)Foci: $( \pm \sqrt { 7 } , 0 )$ 
C) Center: (0, 0)Vertices: (0, ± $2$ )Foci: $( 0 , \pm \sqrt { 7 } )$ 
D) Center: (1, 1)Vertices: (0, ± $2$ )Foci: $( 0 , \pm \sqrt { 7 } )$ 
E) Center: (0, 0)Vertices: (± $2$ , 0)Foci: $( \pm \sqrt { 7 } , 0 )$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = 1 \quad\quad\quad y = -2$

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 0,2 )$ ; directrix: $y = 10$

Find the center, vertices and foci of the hyperbola. $26 y ^ { 2 } - 23 x ^ { 2 } = 598$

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7) Foci: (3, 1), (3, 9)

Using following result find a set of parametric equation of the line. $x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right) , y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$ Line: passes through $( 9,2 )$ and $( - 3,9 )$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 6 )$ ; asymptotes: $y = \pm 6 x$

Select the graph of the following equation. $x y + 4 = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 4,5 ) \quad 7 x + y = 1$

Sketch the graph of the ellipse, using the latera recta. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r ^ { 2 } = 4 \sin 2 \theta$

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates, r > 0.Round your answers to three decimal places. $( 3 , - 2 )$

Identify the conic and select its correct graph. $r = \frac { 9 } { 1 + \cos \theta }$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 3 } { 4 } x$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 18 x - 12 y + 33 = 0$

Convert the rectangular equation to polar form.Assume r > 1. $7 x - y + 6 = 0$

Find the center, vertices and foci of the hyperbola. $3 x ^ { 2 } - 4 y ^ { 2 } = 12$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 10: Topics In Analytic Geometry

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Eccentricity \quad\quad Directrix Ellipse e=1y=−2\quad\quad\quad e = 1 \quad\quad\quad y = -2e=1y=−2

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (0,2)( 0,2 )(0,2) ; directrix: y=10y = 10y=10

Find the center, vertices and foci of the hyperbola. 26y2−23x2=59826 y ^ { 2 } - 23 x ^ { 2 } = 59826y2−23x2=598

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7) Foci: (3, 1), (3, 9)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (0,12)\left( 0 , \frac { 1 } { 2 } \right)(0,21​)

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1) and the line.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±6)( 0 , \pm 6 )(0,±6) ; asymptotes: y=±6xy = \pm 6 xy=±6x

Select the graph of the following equation. xy+4=0x y + 4 = 0xy+4=0

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (4,5)7x+y=1( 4,5 ) \quad 7 x + y = 1(4,5)7x+y=1

Sketch the graph of the ellipse, using the latera recta. x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1

Find the vertex and focus of the parabola. (y−3)2+8(x+6)=0( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0(y−3)2+8(x+6)=0

Select the correct graph of the polar equation.Find an interval for θ\thetaθ for which the graph is traced only once. r2=4sin⁡2θr ^ { 2 } = 4 \sin 2 \thetar2=4sin2θ

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates, r > 0.Round your answers to three decimal places. (3,−2)( 3 , - 2 )(3,−2)

Identify the conic and select its correct graph. r=91+cos⁡θr = \frac { 9 } { 1 + \cos \theta }r=1+cosθ9​

Find the vertex and focus of the parabola. y2=−34xy ^ { 2 } = - \frac { 3 } { 4 } xy2=−43​x

Find the vertex and directrix of the parabola. x2−18x−12y+33=0x ^ { 2 } - 18 x - 12 y + 33 = 0x2−18x−12y+33=0

Convert the rectangular equation to polar form.Assume r > 1. 7x−y+6=07 x - y + 6 = 07x−y+6=0

Find the center, vertices and foci of the hyperbola. 3x2−4y2=123 x ^ { 2 } - 4 y ^ { 2 } = 123x2−4y2=12

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = 1 \quad\quad\quad y = -2$

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 0,2 )$ ; directrix: $y = 10$

Find the center, vertices and foci of the hyperbola. $26 y ^ { 2 } - 23 x ^ { 2 } = 598$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 6 )$ ; asymptotes: $y = \pm 6 x$

Select the graph of the following equation. $x y + 4 = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 4,5 ) \quad 7 x + y = 1$

Sketch the graph of the ellipse, using the latera recta. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r ^ { 2 } = 4 \sin 2 \theta$

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates, r > 0.Round your answers to three decimal places. $( 3 , - 2 )$

Identify the conic and select its correct graph. $r = \frac { 9 } { 1 + \cos \theta }$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 3 } { 4 } x$

Find the vertex and directrix of the parabola. $x ^ { 2 } - 18 x - 12 y + 33 = 0$

Convert the rectangular equation to polar form.Assume r > 1. $7 x - y + 6 = 0$

Find the center, vertices and foci of the hyperbola. $3 x ^ { 2 } - 4 y ^ { 2 } = 12$