Question 1

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places.  $5 x ^ { 2 } - 4 x y + 6 y ^ { 2 } = 9$

Accepted Answer

A)  $\theta = 79.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 81.87 ^ { \circ }$ 
D)  $\theta = 80.87 ^ { \circ }$ 
E)  $\theta = 78.87 ^ { \circ }$ 
A)  $\theta = 79.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 81.87 ^ { \circ }$ 
D)  $\theta = 80.87 ^ { \circ }$ 
E)  $\theta = 78.87 ^ { \circ }$

Question 2

Use a graphing utility to graph the parabola. $$y = 2 x ^ { 2 } + 4 x - 7$$ ​

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 3

Use a graphing utility to graph the parabola. $y = x ^ { 2 } + 4 x - 2$

Accepted Answer

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

Question 4

Find the standard form of the equation of the ellipse with the given characteristics. 
Foci: $( - 5 , - 12 ) , ( - 5 , - 4 )$ , endpoints of the major axis: $( - 5 , - 16 ) , ( - 5,0 )$

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y + 8 ) ^ { 2 } } { 48 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 48 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 48 } = 1$ 
D)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 48 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 48 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$ 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y + 8 ) ^ { 2 } } { 48 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 48 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 48 } = 1$ 
D)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 48 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 48 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$

Question 5

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.

Accepted Answer

A) The maximum distance of $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ and the line through (0,5) is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal. 
C) The maximum distance of $\frac { 1 } { 5 }$ occurs when the slope m is 0 and the line through (0,5) is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal. 
E) The maximum distance of $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5) is horizontal. 
A) The maximum distance of $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ and the line through (0,5) is horizontal. 
B) The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal. 
C) The maximum distance of $\frac { 1 } { 5 }$ occurs when the slope m is 0 and the line through (0,5) is horizontal. 
D) The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal. 
E) The maximum distance of $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5) is horizontal.

Question 6

You and a friend live 4 miles apart (on the same "east-west" street) and are talking on the phone.You hear a clap of thunder from lightning in a storm, and 16 seconds later your friend hears the thunder.Find an equation that gives the possible places where the lightning could have occurred.(Assume that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)

Accepted Answer

A)  $\frac { x ^ { 2 } } { 34,073,600 } + \frac { y ^ { 2 } } { 77,440,000 } = 1$ 
B)  $\frac { x ^ { 2 } } { 34,073,600 } - \frac { y ^ { 2 } } { 77,440,000 } = 1$ 
C)  $\frac { y ^ { 2 } } { 77,440,000 } - \frac { x ^ { 2 } } { 34,073,600 } = 1$ 
D)  $\frac { x ^ { 2 } } { 77,440,000 } - \frac { y ^ { 2 } } { 34,073,600 } = 1$ 
E)  $\frac { x ^ { 2 } } { 77,440,000 } + \frac { y ^ { 2 } } { 34,073,600 } = 1$ 
A)  $\frac { x ^ { 2 } } { 34,073,600 } + \frac { y ^ { 2 } } { 77,440,000 } = 1$ 
B)  $\frac { x ^ { 2 } } { 34,073,600 } - \frac { y ^ { 2 } } { 77,440,000 } = 1$ 
C)  $\frac { y ^ { 2 } } { 77,440,000 } - \frac { x ^ { 2 } } { 34,073,600 } = 1$ 
D)  $\frac { x ^ { 2 } } { 77,440,000 } - \frac { y ^ { 2 } } { 34,073,600 } = 1$ 
E)  $\frac { x ^ { 2 } } { 77,440,000 } + \frac { y ^ { 2 } } { 34,073,600 } = 1$

Question 7

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1$ 
B)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 729 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 54 } + \frac { y ^ { 2 } } { 729 } = 1$ 
E)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 729 } = 1$ 
A)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1$ 
B)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 729 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 54 } + \frac { y ^ { 2 } } { 729 } = 1$ 
E)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 729 } = 1$

Question 8

Use the Quadratic Formula to solve for $y$ .  $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$

Accepted Answer

A)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } - 9 x - 42 \right) } } { 22 }$ 
B)  $y = \frac { ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$ 
C)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$. 
D)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$ 
E)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } + 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$ 
A)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } - 9 x - 42 \right) } } { 22 }$ 
B)  $y = \frac { ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$ 
C)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$. 
D)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } - 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$ 
E)  $y = \frac { - ( 10 x - 10 ) \pm \sqrt { ( 10 x - 10 ) ^ { 2 } + 44 \left( 5 x ^ { 2 } + 9 x - 42 \right) } } { 22 }$

Question 9

Find the graph of the following ellipse.  $4 x ^ { 2 } + 4 y ^ { 2 } - 40 x - 24 y + 120 = 0$

Accepted Answer

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

Question 10

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: $( \pm 2,0 )$ ; asymptotes: $y = \pm 7 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 196 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 196 } = 1$ 
C)  $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 196 } = 1$ 
D)  $\frac { y ^ { 2 } } { 196 } - \frac { x ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 196 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 196 } = 1$ 
B)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 196 } = 1$ 
C)  $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 196 } = 1$ 
D)  $\frac { y ^ { 2 } } { 196 } - \frac { x ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 196 } = 1$

Question 11

Find the Foci of the conic.  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Accepted Answer

A) Foci: $( 0 , \pm \sqrt { 48 } )$ 
B) Foci: $( \pm \sqrt { 8 } , 0 )$ 
C) Foci: $( 0 , \pm \sqrt { 8 } )$ 
D) Foci: $( \pm \sqrt { 48 } , 0 )$ 
E) Foci: $( \sqrt { 8 } , \sqrt { 48 } )$ 
A) Foci: $( 0 , \pm \sqrt { 48 } )$ 
B) Foci: $( \pm \sqrt { 8 } , 0 )$ 
C) Foci: $( 0 , \pm \sqrt { 8 } )$ 
D) Foci: $( \pm \sqrt { 48 } , 0 )$ 
E) Foci: $( \sqrt { 8 } , \sqrt { 48 } )$

Question 12

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

Accepted Answer

The answer of Find the equation of the parabola with...

Question 13

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.  $r = \frac { 2 e } { 1 + e \sin \theta }$

Accepted Answer

A)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$. 
A)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$.

Question 14

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( 0 , - 6 )$

Accepted Answer

A) Polar coordinates: $\left( - 6 , \frac { 3 \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( 6 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 6 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 6 , - \frac { \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 6 , \frac { 3 \pi } { 2 } \right)$ 
A) Polar coordinates: $\left( - 6 , \frac { 3 \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( 6 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 6 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 6 , - \frac { \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 6 , \frac { 3 \pi } { 2 } \right)$

Question 15

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 16

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $\begin{array} { l } 
6 x - 8 y = 8 \
6 x + 8 y = 7
\end{array}$

Accepted Answer

A)  $\Theta \approx 1.3221 \text { radians } \approx 76.7 ^ { \circ }$ 
B)  $\theta \approx 1.3221 \text { radians } \approx 74.7 ^ { \circ }$ 
C)  $\Theta \approx 1.3221 \text { radians } \approx 75.7 ^ { \circ }$ 
D)  $\Theta \approx 1.3221 \text { radians } \approx 77.7 ^ { \circ }$ 
E)  $\theta \approx 1.3221 \text { radians } \approx 73.7 ^ { \circ }$ 
A)  $\Theta \approx 1.3221 \text { radians } \approx 76.7 ^ { \circ }$ 
B)  $\theta \approx 1.3221 \text { radians } \approx 74.7 ^ { \circ }$ 
C)  $\Theta \approx 1.3221 \text { radians } \approx 75.7 ^ { \circ }$ 
D)  $\Theta \approx 1.3221 \text { radians } \approx 77.7 ^ { \circ }$ 
E)  $\theta \approx 1.3221 \text { radians } \approx 73.7 ^ { \circ }$

Question 17

Select the graph of degenerate conic.  $36 x ^ { 2 } - 72 x y + 36 y ^ { 2 } = 0$

Accepted Answer

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

Question 18

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( - \sqrt { 3 } , - \sqrt { 3 } )$

Accepted Answer

A) Polar coordinates: $\left( \sqrt { 6 } , - \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 6 } , - \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 6 } , \frac { 5 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 6 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 6 } , \frac { 3 \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( \sqrt { 6 } , - \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 6 } , - \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 6 } , \frac { 5 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 6 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 6 } , \frac { 3 \pi } { 4 } \right)$

Question 19

Consider the polar equation:  $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ 
Identify the conic without graphing the equation.

Accepted Answer

A)  $e < 1$ , the conic is a parabola. 
B)  $e < 1$ , the conic is a circle. 
C)  $e < 1$ , the conic is a hyperbola. 
D)  $e < 1$ , the conic is an ellipse. 
E) None of the above 
A)  $e < 1$ , the conic is a parabola. 
B)  $e < 1$ , the conic is a circle. 
C)  $e < 1$ , the conic is a hyperbola. 
D)  $e < 1$ , the conic is an ellipse. 
E) None of the above

Question 20

Find a set of parametric equations for the rectangular equation.  $\begin{array} { l } 
t = 5 - x \
y = x ^ { 2 } - 3
\end{array}$

Accepted Answer

A)  $x = t - 5 , y = t ^ { 2 } + 10 t - 22$ 
B)  $x = t - 5 , y = t ^ { 2 } - 10 t + 22$ 
C)  $x = - t + 5 , y = t ^ { 2 } - 22 t + 10$ 
D)  $x = - t + 5 , y = t ^ { 2 } - 10 t + 22$ 
E)  $x = t + 5 , y = t ^ { 2 } - 10 t + 22$ 
A)  $x = t - 5 , y = t ^ { 2 } + 10 t - 22$ 
B)  $x = t - 5 , y = t ^ { 2 } - 10 t + 22$ 
C)  $x = - t + 5 , y = t ^ { 2 } - 22 t + 10$ 
D)  $x = - t + 5 , y = t ^ { 2 } - 10 t + 22$ 
E)  $x = t + 5 , y = t ^ { 2 } - 10 t + 22$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $5 x ^ { 2 } - 4 x y + 6 y ^ { 2 } = 9$

Use a graphing utility to graph the parabola. $y = 2 x ^ { 2 } + 4 x - 7$

Use a graphing utility to graph the parabola. $y = x ^ { 2 } + 4 x - 2$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( - 5 , - 12 ) , ( - 5 , - 4 )$ , endpoints of the major axis: $( - 5 , - 16 ) , ( - 5,0 )$

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.

Use the Quadratic Formula to solve for $y$ . $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$

Find the graph of the following ellipse. $4 x ^ { 2 } + 4 y ^ { 2 } - 40 x - 24 y + 120 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( \pm 2,0 )$ ; asymptotes: $y = \pm 7 x$

Find the Foci of the conic. $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 + e \sin \theta }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 0 , - 6 )$

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

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 6x-8y=8 6x+8y=7

Select the graph of degenerate conic. $36 x ^ { 2 } - 72 x y + 36 y ^ { 2 } = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - \sqrt { 3 } , - \sqrt { 3 } )$

Consider the polar equation: $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ Identify the conic without graphing the equation.

Find a set of parametric equations for the rectangular equation. t=5-x y=-3

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Exam 10: Topics In Analytic Geometry

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 5x2−4xy+6y2=95 x ^ { 2 } - 4 x y + 6 y ^ { 2 } = 95x2−4xy+6y2=9

Use a graphing utility to graph the parabola. y=2x2+4x−7y = 2 x ^ { 2 } + 4 x - 7y=2x2+4x−7 ​

Use a graphing utility to graph the parabola. y=x2+4x−2y = x ^ { 2 } + 4 x - 2y=x2+4x−2

Find the standard form of the equation of the ellipse with the given characteristics. Foci: (−5,−12),(−5,−4)( - 5 , - 12 ) , ( - 5 , - 4 )(−5,−12),(−5,−4) , endpoints of the major axis: (−5,−16),(−5,0)( - 5 , - 16 ) , ( - 5,0 )(−5,−16),(−5,0)

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.

Use the Quadratic Formula to solve for yyy . 5x2+10xy+11y2+9x−10y−42=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 05x2+10xy+11y2+9x−10y−42=0

Find the graph of the following ellipse. 4x2+4y2−40x−24y+120=04 x ^ { 2 } + 4 y ^ { 2 } - 40 x - 24 y + 120 = 04x2+4y2−40x−24y+120=0

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±2,0)( \pm 2,0 )(±2,0) ; asymptotes: y=±7xy = \pm 7 xy=±7x

Find the Foci of the conic. x216+y264=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 116x2​+64y2​=1

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 6).Express the equation in standard form.

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. r=2e1+esin⁡θr = \frac { 2 e } { 1 + e \sin \theta }r=1+esinθ2e​

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (0,−6)( 0 , - 6 )(0,−6)

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​)

Find the angle θ\thetaθ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 6x-8y=8 6x+8y=7

Select the graph of degenerate conic. 36x2−72xy+36y2=036 x ^ { 2 } - 72 x y + 36 y ^ { 2 } = 036x2−72xy+36y2=0

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (−3,−3)( - \sqrt { 3 } , - \sqrt { 3 } )(−3​,−3​)

Consider the polar equation: r=81−0.4cos⁡θr = \frac { 8 } { 1 - 0.4 \cos \theta }r=1−0.4cosθ8​ Identify the conic without graphing the equation.

Find a set of parametric equations for the rectangular equation. t=5-x y=-3

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

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Additional Topics In Trigonometery

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Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $5 x ^ { 2 } - 4 x y + 6 y ^ { 2 } = 9$

Use a graphing utility to graph the parabola. $y = 2 x ^ { 2 } + 4 x - 7$

Use a graphing utility to graph the parabola. $y = x ^ { 2 } + 4 x - 2$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( - 5 , - 12 ) , ( - 5 , - 4 )$ , endpoints of the major axis: $( - 5 , - 16 ) , ( - 5,0 )$

Use the Quadratic Formula to solve for $y$ . $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$

Find the graph of the following ellipse. $4 x ^ { 2 } + 4 y ^ { 2 } - 40 x - 24 y + 120 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( \pm 2,0 )$ ; asymptotes: $y = \pm 7 x$

Find the Foci of the conic. $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 + e \sin \theta }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 0 , - 6 )$

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

Find the angle $\theta$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 6x-8y=8 6x+8y=7

Select the graph of degenerate conic. $36 x ^ { 2 } - 72 x y + 36 y ^ { 2 } = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - \sqrt { 3 } , - \sqrt { 3 } )$

Consider the polar equation: $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ Identify the conic without graphing the equation.