Question 1

Find the center, vertices and foci of the hyperbola. $$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  Center: $( 0,0 )$
Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
B)  Center: $( 0,0 )$
Vertices: $\quad ( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
C)  Center: $( 16,25 )$
Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
D)  Center: $( 16,25 )$
Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
E)  Center: $( 0,0 )$
Vertices: $\quad ( 0 , \pm 4 )$
Foci: $( 0 , \pm \sqrt { 41 } )$ 
A)  Center: $( 0,0 )$
Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
B)  Center: $( 0,0 )$
Vertices: $\quad ( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
C)  Center: $( 16,25 )$
Vertices: $( \pm 4,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
D)  Center: $( 16,25 )$
Vertices: $( \pm 5,0 )$
Foci: $( \pm \sqrt { 41 } , 0 )$ 
E)  Center: $( 0,0 )$
Vertices: $\quad ( 0 , \pm 4 )$
Foci: $( 0 , \pm \sqrt { 41 } )$

Question 2

Identify the conic and select its correct graph. $r = \frac { 10 } { 2 - \cos \theta }$

Accepted Answer

A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $e = \frac { 1 } { 2 }  1 \Rightarrow$ Hyperbola
  
E)  $e = 2 > 1 \Rightarrow$ Hyperbola
  
A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $e = \frac { 1 } { 2 }  1 \Rightarrow$ Hyperbola
  
E)  $e = 2 > 1 \Rightarrow$ Hyperbola

Question 3

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Accepted Answer

A)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar Circle with radius 3
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar 
Circle with radius 3
  
C)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole
Circle with radius 3
  
D)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole axis, pole
Circle with radius 3 
  
E)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole axis, pole
Circle with radius 3

Question 4

Select the curve represented by the parametric equations. (indicate the orientation of the curve) $\begin{array} { l } 
x = 4 - 5 t \
y = 5 + 4 t
\end{array}$

Accepted Answer

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

Question 5

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$x ^ { 2 } + y ^ { 2 } - 7 x + 5 y - 17 = 0$$

Accepted Answer

A)  Circle 
B)  Parabola 
C)  Hyperbola 
D)  Ellipse 
E)  None of the above 
A)  Circle 
B)  Parabola 
C)  Hyperbola 
D)  Ellipse 
E)  None of the above

Question 6

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$

Question 7

Find the vertex, focus, and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

Accepted Answer

A)  Vertex: $\left( - 5 , \frac { 5 } { 2 } \right) ;$ Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
B)  Vertex: $\left( \frac { 5 } { 2 } , - 5 \right) ;$ Focus: $\left( - 5 , \frac { 3 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
C)  Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$; Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
D)  Vertex: $\left( - 5 , \frac { 5 } { 2 } \right) ;$ Focus: $\left( - 5 , \frac { 3 } { 2 } \right) ;$ Directrix: $y = \frac { 7 } { 2 }$ 
E) Vertex: $( 0,0 ) ;$ Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 7 } { 2 }$ 
A)  Vertex: $\left( - 5 , \frac { 5 } { 2 } \right) ;$ Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
B)  Vertex: $\left( \frac { 5 } { 2 } , - 5 \right) ;$ Focus: $\left( - 5 , \frac { 3 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
C)  Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$; Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 3 } { 2 }$ 
D)  Vertex: $\left( - 5 , \frac { 5 } { 2 } \right) ;$ Focus: $\left( - 5 , \frac { 3 } { 2 } \right) ;$ Directrix: $y = \frac { 7 } { 2 }$ 
E) Vertex: $( 0,0 ) ;$ Focus: $\left( - 5 , \frac { 7 } { 2 } \right) ;$ Directrix: $y = \frac { 7 } { 2 }$

Question 8

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.1,1.8 )$

Accepted Answer

A)  Rectangular coordinates: $( 2.0 , - 0.5 )$ 
B)  Rectangular coordinates: $( 0.5 , - 2.0 )$ 
C)  Rectangular coordinates: $( - 0.5,2.0 )$ 
D)  Rectangular coordinates: $( 2.1,1.8 )$ 
E)  Rectangular coordinates: $( - 2.0,0.5 )$ 
A)  Rectangular coordinates: $( 2.0 , - 0.5 )$ 
B)  Rectangular coordinates: $( 0.5 , - 2.0 )$ 
C)  Rectangular coordinates: $( - 0.5,2.0 )$ 
D)  Rectangular coordinates: $( 2.1,1.8 )$ 
E)  Rectangular coordinates: $( - 2.0,0.5 )$

Question 9

Consider a line with slope m and y-intercept $( 0,2 )$ Select the graph of the distance between the origin and the line.

Accepted Answer

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

Question 10

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 11 } { 11 + 16 \sin \theta }$

Accepted Answer

A) 
 
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
B) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
C) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
D) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
E) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
A) 
 
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
B) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
C) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
D) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola 
E) 
  
$e= \frac{16}{11}>1 \Rightarrow $ Hyperabola

Question 11

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 - 6 \cos \theta$

Accepted Answer

A)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
B)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
C)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
D)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$

E)  Symmetric with respect to the polar axis
 $| r | = 11$ when $\theta = \pi$ 
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
A)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
B)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
C)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$
  
D)  Symmetric with respect to the polar axis
$| r | = 11$ when $\theta = \pi$
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$

E)  Symmetric with respect to the polar axis
 $| r | = 11$ when $\theta = \pi$ 
$r = 0$ when $\cos \theta = \frac { 5 } { 6 }$

Question 12

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 6 , \frac { 5 \pi } { 3 } \right)$

Accepted Answer

A)  Rectangular coordinates: $( 3.00,5.20 )$ 
B)  Rectangular coordinates: $( 5.20,3.00 )$ 
C)  Rectangular coordinates: $( 3.00 , - 5.20 )$ 
D)  Rectangular coordinates: $( 3.00,0.05 )$ 
E)  Rectangular coordinates: $( - 5.20,3.00 )$ 
A)  Rectangular coordinates: $( 3.00,5.20 )$ 
B)  Rectangular coordinates: $( 5.20,3.00 )$ 
C)  Rectangular coordinates: $( 3.00 , - 5.20 )$ 
D)  Rectangular coordinates: $( 3.00,0.05 )$ 
E)  Rectangular coordinates: $( - 5.20,3.00 )$

Question 13

Find the vertex and focus of the parabola. 
$y ^ { 2 } = - \frac { 9 } { 8 } x$

Accepted Answer

A)  vertex: $( 0,0 ) \quad$ focus: $\left( - \frac { 9 } { 32 } , 0 \right)$ 
B)  vertex: $( 0,0 )$ focus: $\left( 0 , - \frac { 9 } { 8 } \right)$ 
C)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 9 } { 32 } \right)$ 
D)  vertex: $( 0,0 )$ focus: $\left( - \frac { 9 } { 8 } , 0 \right)$ 
E)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 8 } , - \frac { 9 } { 8 } \right)$ 
A)  vertex: $( 0,0 ) \quad$ focus: $\left( - \frac { 9 } { 32 } , 0 \right)$ 
B)  vertex: $( 0,0 )$ focus: $\left( 0 , - \frac { 9 } { 8 } \right)$ 
C)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 9 } { 32 } \right)$ 
D)  vertex: $( 0,0 )$ focus: $\left( - \frac { 9 } { 8 } , 0 \right)$ 
E)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 8 } , - \frac { 9 } { 8 } \right)$

Question 14

Convert the polar equation to rectangular form. 
$r = 6 \csc \theta$

Accepted Answer

A)  $6 y = r$ 
B)  $y = 6$ 
C)  $x = 6$ 
D)  $y = 6 r$ 
E)  $x = 6 r$ 
A)  $6 y = r$ 
B)  $y = 6$ 
C)  $x = 6$ 
D)  $y = 6 r$ 
E)  $x = 6 r$

Question 15

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 17$

Accepted Answer

A)  $r ^ { 2 } = 17 \sec 2 \theta$ 
B)  $r ^ { 2 } = 34 \csc 2 \theta$ 
C)  $r ^ { 2 } = 34 \cos 2 \theta$ 
D)  $r ^ { 2 } = 17 \csc 2 \theta$ 
E)  $r ^ { 2 } = 34 \sec 2 \theta$ 
A)  $r ^ { 2 } = 17 \sec 2 \theta$ 
B)  $r ^ { 2 } = 34 \csc 2 \theta$ 
C)  $r ^ { 2 } = 34 \cos 2 \theta$ 
D)  $r ^ { 2 } = 17 \csc 2 \theta$ 
E)  $r ^ { 2 } = 34 \sec 2 \theta$

Question 16

Convert the rectangular equation to polar form. Assume $a > 0$ $y = - 6$

Accepted Answer

A)  $r = - 6 \sec \theta$ 
B)  $r = - 6 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 6 \cos \theta$ 
E)  $r = - 6 \sin \theta$ 
A)  $r = - 6 \sec \theta$ 
B)  $r = - 6 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 6 \cos \theta$ 
E)  $r = - 6 \sin \theta$

Question 17

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$x ^ { 2 } + y ^ { 2 } - 6 x + 2 y - 19 = 0$$

Accepted Answer

A)  Circle 
B)  Parabola 
C)  Ellipse 
D)  Hyperbola 
E)  None of the above 
A)  Circle 
B)  Parabola 
C)  Ellipse 
D)  Hyperbola 
E)  None of the above

Question 18

Convert the polar equation to rectangular form. $r ^ { 2 } = 4 \sin \theta$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
E)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
E)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 16 } y ^ { 2 / 3 } = 0$

Question 19

A point in rectangular coordinates is given. Convert the point to polar coordinates.  $( - 3,0 )$

Accepted Answer

A)  Polar coordinates: $( - 3,2 \pi )$ 
B)  Polar coordinates: $( - 3 , \pi )$ 
C)  Polar coordinates: $( 3,2 \pi )$ 
D) Polar coordinates: $\left( 3 , \frac { \pi } { 2 } \right)$ 
E)  Polar coordinates: $( 3 , \pi )$ 
A)  Polar coordinates: $( - 3,2 \pi )$ 
B)  Polar coordinates: $( - 3 , \pi )$ 
C)  Polar coordinates: $( 3,2 \pi )$ 
D) Polar coordinates: $\left( 3 , \frac { \pi } { 2 } \right)$ 
E)  Polar coordinates: $( 3 , \pi )$

Question 20

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 $( 0,0 )$ and $( 9,2 )$

Accepted Answer

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

Find the center, vertices and foci of the hyperbola. $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

Identify the conic and select its correct graph. $r = \frac { 10 } { 2 - \cos \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Select the curve represented by the parametric equations. (indicate the orientation of the curve) x=4-5t y=5+4t

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 7 x + 5 y - 17 = 0$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Find the vertex, focus, and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.1,1.8 )$

Consider a line with slope m and y-intercept $( 0,2 )$ Select the graph of the distance between the origin and the line.

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 11 } { 11 + 16 \sin \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 - 6 \cos \theta$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 6 , \frac { 5 \pi } { 3 } \right)$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 8 } x$

Convert the polar equation to rectangular form. $r = 6 \csc \theta$

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 17$

Convert the rectangular equation to polar form. Assume $a > 0$ $y = - 6$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 6 x + 2 y - 19 = 0$

Convert the polar equation to rectangular form. $r ^ { 2 } = 4 \sin \theta$

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( - 3,0 )$

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 $( 0,0 )$ and $( 9,2 )$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

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Exam 6: Topics in Analytic Geometry

Find the center, vertices and foci of the hyperbola. x225−y216=1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 125x2​−16y2​=1

Identify the conic and select its correct graph. r=102−cos⁡θr = \frac { 10 } { 2 - \cos \theta }r=2−cosθ10​

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=−3r = - 3r=−3

Select the curve represented by the parametric equations. (indicate the orientation of the curve) x=4-5t y=5+4t

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−7x+5y−17=0x ^ { 2 } + y ^ { 2 } - 7 x + 5 y - 17 = 0x2+y2−7x+5y−17=0

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Find the vertex, focus, and directrix of the parabola. (x+5)2=4(y−52)( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)(x+5)2=4(y−25​)

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. (−2.1,1.8)( - 2.1,1.8 )(−2.1,1.8)

Consider a line with slope m and y-intercept (0,2)( 0,2 )(0,2) Select the graph of the distance between the origin and the line.

By using a graphing utility select the correct graph of the polar equation. Identify the graph. 1111+16sin⁡θ\frac { 11 } { 11 + 16 \sin \theta }11+16sinθ11​

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=5−6cos⁡θr = 5 - 6 \cos \thetar=5−6cosθ

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. (6,5π3)\left( 6 , \frac { 5 \pi } { 3 } \right)(6,35π​)

Find the vertex and focus of the parabola. y2=−98xy ^ { 2 } = - \frac { 9 } { 8 } xy2=−89​x

Convert the polar equation to rectangular form. r=6csc⁡θr = 6 \csc \thetar=6cscθ

Convert the rectangular equation to polar form. Assume a>0a > 0a>0 xy=17x y = 17xy=17

Convert the rectangular equation to polar form. Assume a>0a > 0a>0 y=−6y = - 6y=−6

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−6x+2y−19=0x ^ { 2 } + y ^ { 2 } - 6 x + 2 y - 19 = 0x2+y2−6x+2y−19=0

Convert the polar equation to rectangular form. r2=4sin⁡θr ^ { 2 } = 4 \sin \thetar2=4sinθ

A point in rectangular coordinates is given. Convert the point to polar coordinates. (−3,0)( - 3,0 )(−3,0)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Filters

Find the center, vertices and foci of the hyperbola. $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

Identify the conic and select its correct graph. $r = \frac { 10 } { 2 - \cos \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 7 x + 5 y - 17 = 0$

Find the vertex, focus, and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.1,1.8 )$

Consider a line with slope m and y-intercept $( 0,2 )$ Select the graph of the distance between the origin and the line.

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 11 } { 11 + 16 \sin \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 5 - 6 \cos \theta$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 6 , \frac { 5 \pi } { 3 } \right)$

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 8 } x$

Convert the polar equation to rectangular form. $r = 6 \csc \theta$

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 17$

Convert the rectangular equation to polar form. Assume $a > 0$ $y = - 6$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 6 x + 2 y - 19 = 0$

Convert the polar equation to rectangular form. $r ^ { 2 } = 4 \sin \theta$

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( - 3,0 )$