Deck 7: Conic Sections

Question 1

Match the given equation with one of the graphs.
$$x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 16$$

A)

B)

C)

D)

Answer 1

A

Question 2

Match the given equation with one of the graphs.
$25 x ^ { 2 } - 9 y ^ { 2 } = 225$

A)

B)

C)

D)

Answer 2

B

Question 3

Match the given equation with one of the graphs.
$$y ^ { 2 } = - 5 x$$

A)

B)

C)

D)

Answer 3

D

Question 4

Match the given equation with one of the graphs.
$$x ^ { 2 } + y ^ { 2 } + 4 x + 4 y = 0$$

A)

B)

C)

D)

Question 5

Match the given equation with one of the graphs.
$$( x + 3 ) ^ { 2 } = 6 ( y + 3 )$$

A)

B)

C)

D)

Question 6

Match the given equation with one of the graphs.
$$\frac { ( x + 3 ) ^ { 2 } } { 81 } - \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$$

A)

B)

C)

D)

Question 7

Match the system of equations with one of the graphs.
$$\begin{array} { l } 16 x ^ { 2 } + 9 y ^ { 2 } = 144 \\y - x = 4\end{array}$$

A)

B)

C)

D)

Question 8

Match the given equation with one of the graphs.
$$x ^ { 2 } + y ^ { 2 } + 8 x + 8 y = - 28$$

A)

B)

C)

D)

Question 9

Match the given equation with one of the graphs.
$$y ^ { 2 } - x ^ { 2 } = 144$$

A)

B)

C)

D)

Question 10

Match the given equation with one of the graphs.
$$y ^ { 2 } - 9 x ^ { 2 } = 81$$

A)

B)

C)

D)

Question 11

Match the given equation with one of the graphs.
$$y ^ { 2 } = 16 - x ^ { 2 }$$

A)

B)

C)

D)

Question 12

Match the system of inequalities with one of the graphs.
$$\begin{array} { l } x ^ { 2 } + y ^ { 2 } < 25 \\y \geq 1\end{array}$$

A)

B)

C)

D)

Question 13

Match the system of equations with one of the graphs.
$$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 64 \\x ^ { 2 } + y ^ { 2 } = 100\end{array}$$

A)

B)

C)

D)

Question 14

Match the given equation with one of the graphs.
$$x ^ { 2 } = - 4 y$$

A)

B)

C)

D)

Question 15

Match the given equation with one of the graphs.
$$2 x ^ { 2 } - 64 y = 32$$

A)

B)

C)

D)

Question 16

Match the system of equations with one of the graphs.
$$\begin{array} { l } y ^ { 2 } - 4 y = x - 7 \\x y = 3\end{array}$$

A)

B)

C)

D)

Question 17

Match the system of equations with one of the graphs.
$$\begin{array} { l } x ^ { 2 } + y ^ { 2 } + 7 y = 0 \\x ^ { 2 } + y ^ { 2 } = 10 x\end{array}$$

A)

B)

C)

D)

Question 18

Match the given equation with one of the graphs.
$$36 x ^ { 2 } + 49 y ^ { 2 } = 1764$$

A)

B)

C)

D)

Question 19

Match the given equation with one of the graphs.
$$4 x ^ { 2 } + 36 y ^ { 2 } = 144$$

A)

B)

C)

D)

Question 20

Match the system of equations with one of the graphs.
$$\begin{array} { l } 25 x ^ { 2 } + 4 y ^ { 2 } = 100 \\x + y = 5\end{array}$$

A)

B)

C)

D)

Question 21

Match the given equation with one of the graphs.
$x ^ { 2 } = 5 y$

A)

B)

C)

D)

Question 22

Match the given equation with one of the graphs.
$$( y + 3 ) ^ { 2 } = 4 ( x + 4 )$$

A)

B)

C)

D)

Question 23

Match the given equation with one of the graphs.
$$2 y ^ { 2 } - 24 x - 12 = 0$$

A)

B)

C)

D)

Question 24

Match the given equation with one of the graphs.
$$x ^ { 2 } - y ^ { 2 } = 81$$

A)

B)

C)

D)

Question 25

Match the given equation with one of the graphs.
$\frac { ( y - 4 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

A)

B)

C)

D)

Question 26

Match the system of inequalities with one of the graphs.
$$\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 81 \\x + y > 5\end{array}$$

A)

B)

C)

D)

Question 27

Match the given equation with one of the graphs.
$$4 x ^ { 2 } + y ^ { 2 } - 32 x + 60 = 0$$

A)

B)

C)

D)

Question 28

Match the system of equations with one of the graphs.
$$\begin{array} { l } x ^ { 2 } + 4 y ^ { 2 } = 4 \\x ^ { 2 } + y ^ { 2 } = 16\end{array}$$

A)

B)

C)

D)

Question 29

Match the given equation with one of the graphs.
$$( x + 5 ) ^ { 2 } = 4 ( y - 5 )$$

A)

B)

C)

D)

Question 30

Match the given equation with one of the graphs.
$$9 x ^ { 2 } - 36 y ^ { 2 } = 324$$

A)

B)


C)

D)

Question 31

Match the system of equations with one of the graphs.
$$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 121 \\x ^ { 2 } + y ^ { 2 } = 36\end{array}$$

A)

B)

C)

D)

Question 32

Match the system of equations with one of the graphs.
$x y = 36$ $x + y = 12$

A)

B)

C)

D)

Question 33

Match the given equation with one of the graphs.
$$y ^ { 2 } = 3 x$$

A)

B)

C)

D)

Question 34

Match the given equation with one of the graphs.
$$x ^ { 2 } + y ^ { 2 } = 16$$

A)

B)

C)

D)

Question 35

Match the given equation with one of the graphs.
$$4 x ^ { 2 } + 5 y ^ { 2 } - 48 x + 50 y + 249 = 0$$

A)

B)

C)

D)

Question 36

Match the system of inequalities with one of the graphs.
$$\begin{array} { l } y \leq - x ^ { 2 } \\x + y \geq - 2\end{array}$$

A)

B)

C)

D)

Question 37

Match the system of inequalities with one of the graphs.
$$\begin{array} { l } y > x ^ { 2 } - 8 \\2 y - x < - 12\end{array}$$

A)

B)

C)

D)

Question 38

Match the given equation with one of the graphs.
$$x ^ { 2 } + y ^ { 2 } - 4 x - 10 y = - 25$$

A)

B)

C)

D)

Question 39

Match the system of equations with one of the graphs.
$$\begin{array} { l } y = x ^ { 2 } - 6 x - 3 \\7 y - x = 3\end{array}$$

A)

B)

C)

D)

Question 40

Match the given equation with one of the graphs.
$$49 x ^ { 2 } + 25 y ^ { 2 } = 1225$$

A)

B)

C)

D)

Question 41

Match the given equation with one of the graphs.
$$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 100 } = 1$$

A)

B)

C)

D)

Question 42

Match the given equation with one of the graphs.
$$49 x ^ { 2 } + 4 y ^ { 2 } = 196$$

A)

B)

C)

D)

Question 43

Match the system of inequalities with one of the graphs.
$$\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \\y \leq 2 x\end{array}$$

A)

B)

C)

D)

Question 44

Match the given equation with one of the graphs.
$$36 x ^ { 2 } + 9 y ^ { 2 } = 324$$

A)

B)

C)

D)

Question 45

Solve.
Find an equation for the hyperbola with vertices (2, 2)and (2, 8)and e = 12.

Question 46

Match the given equation with one of the graphs.
$$25 x ^ { 2 } + 64 y ^ { 2 } = 1600$$

A)

B)

C)

D)

Question 47

Solve.
Find the eccentricity of an ellipse whose vertices are (-22, 0)and (22, 0)and whose foci are
(-14, 0)and (14, 0).

Question 48

Provide the proper response.
Explain in your own words how you can tell from the equation whether the branches of a
hyperbola open up and down or left and right.

Question 49

Solve.
Find the eccentricity of an ellipse whose vertices are (0, -57)and (0, 57)and whose foci are
(0, -32)and (0, 32).

Question 50

Provide the proper response.
Describe the graph of the equation $$( x - 7 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = - 1$$

Question 51

Match the given equation with one of the graphs.
$$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$$

A)

B)

C)

D)

Question 52

Provide the proper response.
Is the graph of a circle the graph of a function? Explain your answer.

Question 53

Match the system of equations with one of the graphs.
$$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 25 \\x - 5 = 4 y\end{array}$$

A)

B)

C)

D)

Question 54

Solve.
Find an equation for the hyperbola with vertices (4, 1)and (4, 11)and $\mathrm { e } = \frac { 7 } { 5 }$

Question 55

Match the given equation with one of the graphs.
$$( y - 3 ) ^ { 2 } = - 8 ( x + 2 )$$

A)

B)

C)
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D)

Question 56

Match the given equation with one of the graphs.
$$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$$

A)

B)

C)

D)

Question 57

Solve.
Find the eccentricity of the hyperbola given by $$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$$

Question 58

Provide the proper response.
Explain why the graph of a hyperbola does not satisfy the conditions for the graph of a
function.

Question 59

Solve.
Find an equation of an ellipse with vertices (-3,0)and (3, 0)and eccentricity equal to $\frac { 3 } { 9 } .$