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

Question 2

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.  $( - 2.1,1.1 )$

Accepted Answer

A) Rectangular coordinates: (1.9,1.0) 
B) Rectangular coordinates: (-1.0,-1.9) 
C) Rectangular coordinates: (2.1,1.1) 
D) Rectangular coordinates: (-1.9,-1.0) 
E) Rectangular coordinates: (1.0,1.9) 
A) Rectangular coordinates: (1.9,1.0) 
B) Rectangular coordinates: (-1.0,-1.9) 
C) Rectangular coordinates: (2.1,1.1) 
D) Rectangular coordinates: (-1.9,-1.0) 
E) Rectangular coordinates: (1.0,1.9)

Question 3

By using a graphing utility select the correct graph of the polar equation.Identify the graph.  $\frac { 13 } { 13 + 16 \sin \theta }$

Accepted Answer

A)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
B)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
C)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
D)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
E)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
A)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
B)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
C)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
D)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola 
E)    $e =$ $\frac { 16 } { 13 }$ $> 1 \Rightarrow$ Hyperbola

Question 4

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $x = t - 2$ $y = \frac { t } { t - 2 }$

Accepted Answer

A)  $y = x + 2$ 
B)  $y = \frac { x + 2 } { x }$ 
C)  $y = x - 2$ 
D)  $y = \frac { x + 2 } { 3 x }$ 
E)  $y = \frac { x } { x + 2 }$ 
A)  $y = x + 2$ 
B)  $y = \frac { x + 2 } { x }$ 
C)  $y = x - 2$ 
D)  $y = \frac { x + 2 } { 3 x }$ 
E)  $y = \frac { x } { x + 2 }$

Question 5

Select the graph of degenerate conic.  $9 x ^ { 2 } - 2 x y + 9 y ^ { 2 } = 0$

Accepted Answer

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

Question 6

Select the curve represented by the parametric equations.  $\begin{array} { l } 
x = 5 \cos \theta \
y = 6 \sin \theta
\end{array}$

Accepted Answer

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

Question 7

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( - 4,7 )$

Accepted Answer

A)  $x ^ { 2 } = \frac { - 4 } { 49 } y$ 
B)  $y ^ { 2 } = \frac { - 4 } { 49 } x$ 
C)  $y ^ { 2 } = \frac { 49 } { - 4 } x$ 
D)  $x ^ { 2 } = \frac { 49 } { - 4 } y$ 
E)  $y ^ { 2 } = x$ 
A)  $x ^ { 2 } = \frac { - 4 } { 49 } y$ 
B)  $y ^ { 2 } = \frac { - 4 } { 49 } x$ 
C)  $y ^ { 2 } = \frac { 49 } { - 4 } x$ 
D)  $x ^ { 2 } = \frac { 49 } { - 4 } y$ 
E)  $y ^ { 2 } = x$

Question 8

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.)    $a = 4.5$

Accepted Answer

A)  $x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 18 x$ 
B)  $x ^ { 2 } = \frac { 1 } { 18 } y \text { or } y = 18 x ^ { 2 }$ 
C)  $x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 4.5 x$ 
D)  $x ^ { 2 } = 18 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }$ 
E)  $x ^ { 2 } = 4.5 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }$ 
A)  $x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 18 x$ 
B)  $x ^ { 2 } = \frac { 1 } { 18 } y \text { or } y = 18 x ^ { 2 }$ 
C)  $x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 4.5 x$ 
D)  $x ^ { 2 } = 18 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }$ 
E)  $x ^ { 2 } = 4.5 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }$

Question 9

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.  $16 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 0$

Accepted Answer

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

Question 10

Identify the conic and select its correct graph.  $r = \frac { 6 } { 1 - \cos \theta }$

Accepted Answer

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

Question 11

Select the correct graph of the polar equation.Describe your viewing window.  $r = \frac { 9 \pi } { 2 }$

Accepted Answer

A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 18 \
X _ { \max } = 18 \
X _ { s c l } = 3 \
Y _ { \min } = - 18 \
Y _ { \max } = 18 \
Y _ { s c l } = 3
\end{array}$

Question 12

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -4)

Accepted Answer

A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x 
A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x

Question 13

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 4 ( 1 - \cos \theta )$

Accepted Answer

A) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
B) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
C) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
D) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
E) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
A) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
B) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
C) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
D) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$   
E) Symmetric with respect to polar axis $\begin{array} { l } 
| r | = 8 \text { when } \theta = \pi \
r = 0 \text { when } \theta = 0
\end{array}$

Question 14

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

Accepted Answer

A)    $0 < \theta < \infty$ 
B)    $0 < \theta < \infty$ 
C)    $0 < \theta < \infty$ 
D)    $0 < \theta < \infty$ 
E)    $0 < \theta < \infty$ 
A)    $0 < \theta < \infty$ 
B)    $0 < \theta < \infty$ 
C)    $0 < \theta < \infty$ 
D)    $0 < \theta < \infty$ 
E)    $0 < \theta < \infty$

Question 15

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ; vertical axis

Accepted Answer

A)  $x ^ { 2 } = 75 y$ 
B)  $x ^ { 2 } = - 75 y$ 
C)  $y ^ { 2 } = - 75 x$ 
D)  $y ^ { 2 } = 75 x$ 
E)  $x ^ { 2 } = \frac { y } { 75 }$ 
A)  $x ^ { 2 } = 75 y$ 
B)  $x ^ { 2 } = - 75 y$ 
C)  $y ^ { 2 } = - 75 x$ 
D)  $y ^ { 2 } = 75 x$ 
E)  $x ^ { 2 } = \frac { y } { 75 }$

Question 16

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.  $( 8.98,3.0 )$

Accepted Answer

A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50) 
A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50)

Question 17

Use the Quadratic Formula to solve for $y$ .  $14 x ^ { 2 } - 10 x y + 9 y ^ { 2 } - 41 = 0$

Accepted Answer

A)  $y = \frac { 14 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( x ^ { 2 } - 9 \right) } } { - 18 }$ 
B)  $y = \frac { 14 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( x ^ { 2 } + 9 \right) } } { 18 }$ 
C)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( 14 x ^ { 2 } - 41 \right) } } { - 18 }$ 
D)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( 14 x ^ { 2 } + 41 \right) } } { 18 }$ 
E)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } - 36 \left( 14 x ^ { 2 } - 41 \right) } } { 18 }$ 
A)  $y = \frac { 14 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( x ^ { 2 } - 9 \right) } } { - 18 }$ 
B)  $y = \frac { 14 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( x ^ { 2 } + 9 \right) } } { 18 }$ 
C)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( 14 x ^ { 2 } - 41 \right) } } { - 18 }$ 
D)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } + 36 \left( 14 x ^ { 2 } + 41 \right) } } { 18 }$ 
E)  $y = \frac { 10 x \pm \sqrt { 100 x ^ { 2 } - 36 \left( 14 x ^ { 2 } - 41 \right) } } { 18 }$

Question 18

A projectile is launched at a height of h feet above the ground 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 $x = \left( v _ { 0 } \cos \theta \right) t \text { and } y = h + \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . Select the correct graph of the path of a projectile launched from ground level at the value of $\theta$ and $v _ { 0 }$ .
 $\theta = 15 ^ { \circ } , v _ { 0 } = 80$ feet per second

Accepted Answer

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

Question 19

Identify the conic and select its correct graph.  $r = \frac { 2.9 } { 2.9 - \cos \theta }$

Accepted Answer

A)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
B)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
C)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ E  
D)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
E)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ E  
A)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
B)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
C)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ E  
D)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ Ellipse   
E)  $e = \frac { 1 } { 2.9 } < 1 \Rightarrow$ E

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 $( 5,8 )$

Accepted Answer

A)  $x = 8 t , y = 5 t$ 
B)  $x = 5 t , y = - 8 t$ 
C)  $x = - 5 t , y = - t$ 
D)  $x = - 5 t , y = 8 t$ 
E)  $x = 5 t , y = 8 t$ 
A)  $x = 8 t , y = 5 t$ 
B)  $x = 5 t , y = - 8 t$ 
C)  $x = - 5 t , y = - t$ 
D)  $x = - 5 t , y = 8 t$ 
E)  $x = 5 t , y = 8 t$

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

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 2.1,1.1 )$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 13 } { 13 + 16 \sin \theta }$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t - 2$ $y = \frac { t } { t - 2 }$

Select the graph of degenerate conic. $9 x ^ { 2 } - 2 x y + 9 y ^ { 2 } = 0$

Select the curve represented by the parametric equations. x=5\theta y=6\theta

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( - 4,7 )$

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.) $a = 4.5$

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. $16 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 0$

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 - \cos \theta }$

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { 9 \pi } { 2 }$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -4)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 ( 1 - \cos \theta )$

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ; vertical axis

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 8.98,3.0 )$

Use the Quadratic Formula to solve for $y$ . $14 x ^ { 2 } - 10 x y + 9 y ^ { 2 } - 41 = 0$

Identify the conic and select its correct graph. $r = \frac { 2.9 } { 2.9 - \cos \theta }$

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 $( 5,8 )$

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

Exam 10: 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

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. (−2.1,1.1)( - 2.1,1.1 )(−2.1,1.1)

By using a graphing utility select the correct graph of the polar equation.Identify the graph. 1313+16sin⁡θ\frac { 13 } { 13 + 16 \sin \theta }13+16sinθ13​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t−2x = t - 2x=t−2 y=tt−2y = \frac { t } { t - 2 }y=t−2t​

Select the graph of degenerate conic. 9x2−2xy+9y2=09 x ^ { 2 } - 2 x y + 9 y ^ { 2 } = 09x2−2xy+9y2=0

Select the curve represented by the parametric equations. x=5\theta y=6\theta

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point (−4,7)( - 4,7 )(−4,7)

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.) a=4.5a = 4.5a=4.5

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. 16x2+9y2−98x+5y+224=016 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 016x2+9y2−98x+5y+224=0

Identify the conic and select its correct graph. r=61−cos⁡θr = \frac { 6 } { 1 - \cos \theta }r=1−cosθ6​

Select the correct graph of the polar equation.Describe your viewing window. r=9π2r = \frac { 9 \pi } { 2 }r=29π​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -4)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4(1−cos⁡θ)r = 4 ( 1 - \cos \theta )r=4(1−cosθ)

Select the correct graph of the polar equation.Find an interval for θ\thetaθ for which the graph is traced only once. r2=4θr ^ { 2 } = \frac { 4 } { \theta }r2=θ4​

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (−5,13)\left( - 5 , \frac { 1 } { 3 } \right)(−5,31​) ; vertical axis

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. (8.98,3.0)( 8.98,3.0 )(8.98,3.0)

Use the Quadratic Formula to solve for yyy . 14x2−10xy+9y2−41=014 x ^ { 2 } - 10 x y + 9 y ^ { 2 } - 41 = 014x2−10xy+9y2−41=0

Identify the conic and select its correct graph. r=2.92.9−cos⁡θr = \frac { 2.9 } { 2.9 - \cos \theta }r=2.9−cosθ2.9​

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

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 2.1,1.1 )$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 13 } { 13 + 16 \sin \theta }$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t - 2$ $y = \frac { t } { t - 2 }$

Select the graph of degenerate conic. $9 x ^ { 2 } - 2 x y + 9 y ^ { 2 } = 0$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( - 4,7 )$

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.) $a = 4.5$

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. $16 x ^ { 2 } + 9 y ^ { 2 } - 98 x + 5 y + 224 = 0$

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 - \cos \theta }$

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { 9 \pi } { 2 }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 ( 1 - \cos \theta )$

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ; vertical axis

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 8.98,3.0 )$

Use the Quadratic Formula to solve for $y$ . $14 x ^ { 2 } - 10 x y + 9 y ^ { 2 } - 41 = 0$

Identify the conic and select its correct graph. $r = \frac { 2.9 } { 2.9 - \cos \theta }$