Question 1

Identify the conic as a circle or an ellipse then find the center.
​ $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$$ ​

Accepted Answer

Ellipse
Center: $$( 0,0 )$$

Question 2

Identify the conic by writing the equation in standard form.
​ $4 x ^ { 2 } + 9 y ^ { 2 } + 16 x - 90 y + 205 = 0$ ​

Accepted Answer

$$\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$$ ; ellipse

Question 3

Find a polar equation of the conic with its focus at the pole.
​
Conics
Eccentricity
Directrix
Hyperbola $e = \frac { 3 } { 2 }$ $x = - 4$ ​

Accepted Answer

$r = \frac { 8 } { 2 - 3 \cos \theta }$

Question 4

Graph the hyperbola.
​ $9 x ^ { 2 } - 25 y ^ { 2 } = 225$ ​

Accepted Answer

The answer of Graph the hyperbola.
​ \(9 x ^ {...

Question 5

Graph the hyperbola.
​ $$9 y ^ { 2 } - 9 x ^ { 2 } + 72 y + 54 x = 18$$ ​

Accepted Answer

The answer of Graph the hyperbola.
​ \[9 y ^ {...

Question 6

Find a polar equation of the conic with its focus at the pole.
​
Conics
Vertex or vertices
Parabola $\left( 5 , - \frac { \pi } { 2 } \right)$ ​

Accepted Answer

The answer of Find a polar equation of the conic...

Question 7

Select the polar equation of graph.
​   ​

Accepted Answer

The answer of Select the polar equation of graph.
​ ...

Question 8

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.
​
Passes through the point $\left( - 3 , \frac { 1 } { 4 } \right)$ ; vertical axis
​

Accepted Answer

The answer of Find the standard form of the equation...

Question 9

Describe the graph of the polar equation and find the corresponding rectangular equation. Select the correct graph.
​ $$r = 5 \sec \theta$$ ​

Accepted Answer

The graph of the polar equatio

Question 10

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 4,000 miles.)
​   Find the distance between the surface of the Earth and the satellite when $\theta = 40 ^ { \circ }$ .
​

Accepted Answer

Distance between sur

Question 11

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
​ $x = t + 1$ $y = \frac { t } { t + 1 }$ ​

Accepted Answer

The answer of Eliminate the parameter and write the corresponding...

Question 12

Find the standard form of the equation of the ellipse with the given characteristics.
​
Foci: $( 0,0 ) , ( 8,0 )$ ; major axis of length 10.
​

Accepted Answer

The answer of Find the standard form of the equation...

Question 13

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.
​ $$\frac { ( y + 4 ) ^ { 2 } } { \frac { 1 } { 64 } } - \frac { ( x - 2 ) ^ { 2 } } { \frac { 1 } { 49 } } = 1$$ ​

Accepted Answer

The answer of Select the correct graph of the following...

Question 14

Find a set of parametric equations for the rectangular equation.
​ $\begin{array} { l } 
t = 3 - x \
x = 4 y - 3
\end{array}$ ​

Accepted Answer

The answer of Find a set of parametric equations for...

Question 15

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

Accepted Answer

The answer of Find the standard form of the equation...

Identify the conic as a circle or an ellipse then find the center. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the conic by writing the equation in standard form. $4 x ^ { 2 } + 9 y ^ { 2 } + 16 x - 90 y + 205 = 0$

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Hyperbola $e = \frac { 3 } { 2 }$ $x = - 4$

Graph the hyperbola. $9 x ^ { 2 } - 25 y ^ { 2 } = 225$

Graph the hyperbola. $9 y ^ { 2 } - 9 x ^ { 2 } + 72 y + 54 x = 18$

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola $\left( 5 , - \frac { \pi } { 2 } \right)$

Select the polar equation of graph.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point $\left( - 3 , \frac { 1 } { 4 } \right)$ ; vertical axis

Describe the graph of the polar equation and find the corresponding rectangular equation. Select the correct graph. $r = 5 \sec \theta$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 1$ $y = \frac { t } { t + 1 }$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 0,0 ) , ( 8,0 )$ ; major axis of length 10.

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. $\frac { ( y + 4 ) ^ { 2 } } { \frac { 1 } { 64 } } - \frac { ( x - 2 ) ^ { 2 } } { \frac { 1 } { 49 } } = 1$

Find a set of parametric equations for the rectangular equation. t=3-x x=4y-3

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

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Limits of Functions

Filters

Exam 10: Topics From Analytic Geometry

Identify the conic as a circle or an ellipse then find the center. ​ x236+y225=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 136x2​+25y2​=1 ​

Identify the conic by writing the equation in standard form. ​ 4x2+9y2+16x−90y+205=04 x ^ { 2 } + 9 y ^ { 2 } + 16 x - 90 y + 205 = 04x2+9y2+16x−90y+205=0 ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentricity Directrix Hyperbola e=32e = \frac { 3 } { 2 }e=23​ x=−4x = - 4x=−4 ​

Graph the hyperbola. ​ 9x2−25y2=2259 x ^ { 2 } - 25 y ^ { 2 } = 2259x2−25y2=225 ​

Graph the hyperbola. ​ 9y2−9x2+72y+54x=189 y ^ { 2 } - 9 x ^ { 2 } + 72 y + 54 x = 189y2−9x2+72y+54x=18 ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola (5,−π2)\left( 5 , - \frac { \pi } { 2 } \right)(5,−2π​) ​

Select the polar equation of graph. ​ ​

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Passes through the point (−3,14)\left( - 3 , \frac { 1 } { 4 } \right)(−3,41​) ; vertical axis ​

Describe the graph of the polar equation and find the corresponding rectangular equation. Select the correct graph. ​ r=5sec⁡θr = 5 \sec \thetar=5secθ ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​ x=t+1x = t + 1x=t+1 y=tt+1y = \frac { t } { t + 1 }y=t+1t​ ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: (0,0),(8,0)( 0,0 ) , ( 8,0 )(0,0),(8,0) ; major axis of length 10. ​

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. ​ (y+4)2164−(x−2)2149=1\frac { ( y + 4 ) ^ { 2 } } { \frac { 1 } { 64 } } - \frac { ( x - 2 ) ^ { 2 } } { \frac { 1 } { 49 } } = 1641​(y+4)2​−491​(x−2)2​=1 ​

Find a set of parametric equations for the rectangular equation. ​ t=3-x x=4y-3 ​

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

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Limits of Functions

Filters

Identify the conic as a circle or an ellipse then find the center. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the conic by writing the equation in standard form. $4 x ^ { 2 } + 9 y ^ { 2 } + 16 x - 90 y + 205 = 0$

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Hyperbola $e = \frac { 3 } { 2 }$ $x = - 4$

Graph the hyperbola. $9 x ^ { 2 } - 25 y ^ { 2 } = 225$

Graph the hyperbola. $9 y ^ { 2 } - 9 x ^ { 2 } + 72 y + 54 x = 18$

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola $\left( 5 , - \frac { \pi } { 2 } \right)$

Select the polar equation of graph.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point $\left( - 3 , \frac { 1 } { 4 } \right)$ ; vertical axis

Describe the graph of the polar equation and find the corresponding rectangular equation. Select the correct graph. $r = 5 \sec \theta$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 1$ $y = \frac { t } { t + 1 }$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 0,0 ) , ( 8,0 )$ ; major axis of length 10.

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. $\frac { ( y + 4 ) ^ { 2 } } { \frac { 1 } { 64 } } - \frac { ( x - 2 ) ^ { 2 } } { \frac { 1 } { 49 } } = 1$

Find a set of parametric equations for the rectangular equation. t=3-x x=4y-3

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