Deck 10: Conic Sections

Question 1

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.
$y = - 4 x ^ { 2 }$

A) $\operatorname { vertex } ( 0,0 )$


B) $\text { vertex } ( 0 , - 4 )$


C) $\text { vertex } ( 0,0 )$


D) $\text { vertex } ( 0,0 )$

Answer 1

A

Question 2

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
$x^{2}+y^{2}=36$

A) center $( 0,0 )$ ; radius $= 6$


B) center $( 0,0 ) ;$ radius $= \sqrt { 6 }$

Answer 2

A

Question 3

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
$$x ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$$

A) center $( - 4,0 )$ ; radius $= 3$

B) center $( 0,4 )$ ; radius $= 3$

C) center $( 4,0 )$ ; radius $= 3$

D) center $( 0 , - 4 )$ ; radius $= 3$

Answer 3

D

Question 4

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( - 5,6 )$


B) $\text { vertex } ( 5 , - 6 )$


C) $\text { vertex } ( - 6 , - 5 )$


D) $\text { vertex } ( - 5 , - 6 )$

Question 5

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 0,3 )$ ; radius $= 3$

B) center $( - 0 , - 3 )$ ; radius $= 3$

C) center $( 3,0 )$ ; radius $= 3$

D) center $( - 3 , - 0 )$ ; radius $= 3$

Question 6

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 4 , - 1 )$ ; radius $= 4$

B) center $( - 4,1 )$ ; radius $= 4$

C) center $( 4,1 )$ ; radius $= 4$

D) center $( - 4 , - 1 )$ ; radius $= 4$

Question 7

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 2 , - 1 )$ ; radius $= 4$

B) center $( 2,1 )$ ; radius $= 4$

C) center $( - 2 , - 1 )$ ; radius $= 4$

D) center $( - 2,1 )$ ; radius $= 4$

Question 8

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( - 4,5 )$


B) $\text { vertex } ( 5 , - 4 )$


C)
D) $\operatorname { vertex } ( - 5,4 )$

Question 9

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.
$x = 3 ( y + 6 ) ^ { 2 } + 5$

A) $\text { vertex }(5,6)$


B) $\text { vertex } ( 5 , - 6 )$


C) $\text { vertex } ( 5 , - 6 )$


D) $\text { vertex } ( - 6,5 )$

Question 10

A) $\operatorname { vertex } ( 0,0 )$


B) vertex $( 0,0 )$

C) vertex $( 0,0 )$


D) vertex $( - 2,0 )$

Question 11

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( 4,2 )$


B) $\text { vertex } ( - 4 , - 2 )$


C) $\text { vertex } ( 2,4 )$


D) $\text { vertex } ( - 4,2 )$

Question 12

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.
$y = x ^ { 2 } + 4 x + 8$

A) $\text { vertex } ( 2,4 )$


B)
C) $\text { vertex } ( - 2,4 )$


D) $\text { vertex } ( 4 , - 2 )$

Question 13

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 0,0 )$ ; radius $= 1$

B) center $( 7,7 )$ ; radius $= \sqrt { 7 }$

C) center $( 0,0 )$ ; radius $= 7$

D) center $( 0,0 )$ ; radius $= \sqrt { 7 }$

Question 14

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.
$y = x ^ { 2 } + 3$

A) $\text { vertex } ( 0,3 )$


B) $\operatorname { vertex } ( 3,0 )$


C) $\text { vertex } ( 0 , - 3 )$


D) $\text { vertex } ( - 3,0 )$

Question 15

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 0 , - 4 )$ ; radius $= 3$

B) center $( 0,4 )$ ; radius $= 3$

C) center $( - 4,0 )$ ; radius $= 3$

D) center $( 4,0 )$ ; radius $= 3$

Question 16

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( 3,4 )$


B) $\text { vertex } ( - 4 , - 3 )$


C) $\text { vertex } ( - 3 , - 4 )$


D) $\text { vertex } ( - 3,4 )$

Question 17

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( - 5 , - 3 )$


B) $\text { vertex } ( 3,5 )$


C) $\text { vertex } ( - 3 , - 5 )$


D) $\text { vertex } ( 5 , - 3 )$

Question 18

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.

A) $\text { vertex } ( 0,2 )$


B) $\text { vertex } ( 2,0 )$


C) $\text { vertex } ( 0 , - 2 )$


D) $\text { vertex } ( - 2,0 )$

Question 19

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\operatorname { vertex } ( - 4,1 )$


B) $\text { vertex } ( 1 , - 4 )$


C) $\text { vertex } ( 4 , - 1 )$


D) $\text { vertex } ( 4 , - 1 )$

Question 20

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center andradius.

A) $\text { vertex } ( 2 , - 3 )$


B)
C) $\text { vertex } ( 3 , - 2 )$


D) $\text { vertex } ( 2 , - 3 )$

Question 21

Find the center and the radius of the circle.
$$x ^ { 2 } + ( y - 1 ) ^ { 2 } = 7$$

A) center $( 0,1 )$ ; radius $= 49$
B) center $( 0,1 ) ;$ radius $= 7$
C) center $( 0,1 )$ ; radius $= \sqrt { 7 }$
D) center $( 1,0 )$ ; radius $= \sqrt { 7 }$

Question 22

Find the center and the radius of the circle.
$$7 x ^ { 2 } + 7 y ^ { 2 } = 49$$

A) center $( 7,7 )$ , radius $= \sqrt { 7 }$
B) center $( 0,0 )$ , radius $= 7$
C) center $( 0,0 )$ , radius $= \sqrt { 7 }$
D) center $( 0,0 )$ , radius $= 49$

Question 23

Find the center and the radius of the circle.
$$( x + 8 ) ^ { 2 } + y ^ { 2 } = 36$$

A) center $( 0 , - 8 )$ ; radius $= 6$
B) center $( - 8,0 )$ ; radius $= 6$
C) center $( 8,0 )$ ; radius $= 6$
D) center $( - 8,0 )$ ; radius $= 36$

Question 24

Write an equation of the circle with the given center and radius.
$$( 0 , - 6 ) ; 6$$

A) $( x + 6 ) ^ { 2 } + y ^ { 2 } = 36$
B) $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 36$
C) $( x - 6 ) ^ { 2 } + y ^ { 2 } = 36$
D) $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 6$

Question 25

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( - 3,3 )$ ; radius $= 2$

B) center $( 3,3 )$ ; radius $= 2$

C) center $( 3 , - 3 )$ ; radius $= 2$

D) center $( - 3 , - 3 )$ ; radius $= 2$

Question 26

Find the center and the radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 18 x + 6 y + 54 = 0$$

A) center $( - 9,3 )$ , radius $= 36$
B) center $( 9 , - 3 )$ , radius $= 6$
C) center $( - 3,9 )$ , radius $= 6$
D) center $( 3 , - 9 )$ , radius $= 36$

Question 27

Find the center and the radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 10 = 9$$

A) center $( - 1 , - 3 )$ , radius $= 9$
B) center $( 3,1 )$ , radius $= 3$
C) center $( 1,3 )$ , radius $= 3$
D) center $( - 3 , - 1 )$ , radius $= 9$

Question 28

Solve.
An amusement park has a Ferris wheel with a height of 72 meters and a diameter of 68 meters. Using the drawing, write the equation of the wheel.

A) $x ^ { 2 } + y ^ { 2 } = 34 ^ { 2 }$
B) $x ^ { 2 } + ( y - 38 ) ^ { 2 } = 34 ^ { 2 }$
C) $x ^ { 2 } + ( y + 38 ) ^ { 2 } = 34 ^ { 2 }$
D) $x ^ { 2 } + ( y - 38 ) ^ { 2 } = 68 ^ { 2 }$

Question 29

Write an equation of the circle with the given center and radius.
$( 8,7 ) ; 8$

A) $( x - 7 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 8$
B) $( x + 8 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 64$
C) $( x + 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 8$
D) $( x - 8 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 64$

Question 30

Write an equation of the circle with the given center and radius.
$( 6,1 ) ; \sqrt { 14 }$

A) $( x - 6 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 14$
B) $( x - 1 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 196$
C) $( x + 1 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 196$
D) $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 14$

Question 31

Write an equation of the circle with the given center and radius.
$( - 8,0 ) ; 7$

A) $x ^ { 2 } + ( y + 8 ) ^ { 2 } = 7$
B) $( x - 8 ) ^ { 2 } + y ^ { 2 } = 49$
C) $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 7$
D) $( x + 8 ) ^ { 2 } + y ^ { 2 } = 49$

Question 32

Find the center and the radius of the circle.
$$\mathrm { x } ^ { 2 } + ( \mathrm { y } + 8 ) ^ { 2 } = 49$$

A) center $( 0,8 )$ ; radius $= 7$
B) center $( 0 , - 8 )$ ; radius $= 7$
C) center $( - 8,0 )$ ; radius $= 7$
D) center $( 0 , - 8 )$ ; radius $= 49$

Question 33

Find the center and the radius of the circle.
$$( x + 5 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 15$$

A) center $( - 5,9 )$ ; radius $= 15$
B) center $( 5 , - 9 )$ ; radius $= \sqrt { 15 }$
C) center $( - 5,9 )$ ; radius $= 225$
D) center $( - 5,9 )$ ; radius $= \sqrt { 15 }$

Question 34

Solve.
A bridge constructed over a river has a supporting arch in the shape of a parabola. The length of the road over the parabolic arch is 300 feet and the maximum height of the arch is 134 feet. Write the equation of the arch.

A) $y = - x ^ { 2 } + 134$
B) $y = x ^ { 2 } + 134$
C) $y = \frac { 67 } { 11,250 } x ^ { 2 } + 134$
D) $y = - \frac { 67 } { 11,250 } x ^ { 2 } + 134$

Question 35

Find the center and the radius of the circle.
$$x ^ { 2 } + y ^ { 2 } + 12 x - 2 y + 33 = 0$$

A) center $( 6 , - 1 )$ , radius $= 4$
B) center $( - 6,1 )$ , radius $= 4$
C) center $( - 6,1 )$ , radius $= 2$
D) center $( 6 , - 1 )$ , radius $= 2$

Question 36

Write an equation of the circle with the given center and radius.
$( 0,1 ) ; \sqrt { 11 }$

A) $( x + 1 ) ^ { 2 } + y ^ { 2 } = 121$
B) $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 11$
C) $x ^ { 2 } + ( y + 1 ) ^ { 2 } = 11$
D) $( x - 1 ) ^ { 2 } + y ^ { 2 } = 121$

Question 37

Write an equation of the circle with the given center and radius.
the origin; $\sqrt { 3 }$

A) $x ^ { 2 } + y ^ { 2 } = \sqrt { 3 }$
B) $x ^ { 2 } + y ^ { 2 } = 3$
C) $x ^ { 2 } + y ^ { 2 } = \frac { 3 } { 4 }$
D) $x ^ { 2 } + y ^ { 2 } = 9$

Question 38

Find the center and the radius of the circle.
$$( x + 9 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 25$$

A) center $( - 5 , - 9 )$ ; radius $= 5$
B) center $( - 9 , - 5 ) ;$ radius $= 5$
C) center $( 5,9 )$ ; radius $= 25$
D) center $( 9,5 )$ ; radius $= 25$

Question 39

Write an equation of the circle with the given center and radius.
$( 0,0 ) ; 14$

A) $x ^ { 2 } + y ^ { 2 } = 14$
B) $x ^ { 2 } + y ^ { 2 } = 196$
C) $x ^ { 2 } - y ^ { 2 } = 14$
D) $x ^ { 2 } + y ^ { 2 } = 28$

Question 40

The graph of the equation is a circle. Find the center and the radius, and then graph the circle.
A) center $( 1,2 ) ;$ radius $= 2 \sqrt { 6 }$

B) center $( 1 , - 2 )$ ; radius $= 2 \sqrt { 6 }$

C) center $( - 1,2 )$ ; radius $= 2 \sqrt { 6 }$

D) center $( - 1,2 )$ ; radius $= 24$

Question 41

Graph the equation.
$x^{2}-4 y^{2}=4$

A)

B)

C)

D)

Question 42

Graph the equation.
$25 x^{2}+16 y^{2}=400$

A)

B)

C)

D)

Question 43

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 113 \\x + y = - 15\end{array} \right.$$

A) $( 7 , - 8 ) , ( 8 , - 7 )$
В) $( - 7 , - 8 ) , ( - 8 , - 7 )$
C) $( 7,8 ) , ( 8,7 )$
D) $( - 7,8 ) , ( - 8,7 )$

Question 44

Graph the equation.
$$\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x + 1 ) ^ { 2 } } { 36 } = 1$$

A)

B)

C)


D)

Question 45

Graph the equation.
$$\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$$

A)

B)

C)

D)

Question 46

Graph the equation.
$16 x^{2}+y^{2}=16$

A)

B)

C)

D)

Question 47

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

A)

B)

C)

D)

Question 48

Graph the equation.
$4 y^{2}-9 x^{2}=36$

A)

B)

C)

D)

Question 49

Graph the equation.
$$\frac { ( x + 1 ) ^ { 2 } } { 16 } - \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$$

A)

B)

C)

D)

Question 50

Graph the equation.
$x^{2}+16 y^{2}=16$

A)

B)

C)

D)

Question 51

Graph the equation.
$$\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

A)

B)

C)

D)

Question 52

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = - 8 \\y & = x\end{aligned} \right.$$

A) $( 2 , - 2 )$
B) $( 2,2 )$
C) $( 2 , - 2 ) , ( - 2,2 )$
D) $( 2,2 ) , ( - 2 , - 2 )$

Question 53

Graph the equation.
$\frac{y^{2}}{4}-\frac{x^{2}}{25}=1$

A)


B)
C)

D)

Question 54

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 40 \\2 x + 6 y = 0\end{array} \right.$$

A) $( 6 , - 2 )$
B) $( 6 , - 2 ) , ( - 6 , - 2 )$
C) $( 6 , - 2 ) , ( - 6,2 )$
D) $( 6,2 ) , ( - 6 , - 2 )$

Question 55

Graph the equation.
$$\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 1$$

A)

B)

C)


D)

Question 56

Graph the equation.
$9 x^{2}+25 y^{2}=225$

A)

B)


C)

D)

Question 57

Graph the equation.
$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$$

A)

B)

C)


D)

Question 58

Graph the equation.
$$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$$

A)

B)

C)

D)

Question 59

Graph the equation.
$y^{2}-16 x^{2}=16$

A)

B)

C)

D)

Question 60

Graph the equation.
$\frac{x^{2}}{4}+\frac{y^{2}}{25}=1$

A)

B)

C)

D)

Question 61

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } 5 x ^ { 2 } - 4 y ^ { 2 } = 64 \\4 x ^ { 2 } + 4 y ^ { 2 } = 80\end{array} \right.$$

A) $( 4 , - 2 ) , ( 4,2 )$
B) $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$
C) $( - 4 , - 2 ) , ( - 2 , - 4 )$
D) $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$

Question 62

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 85 \\x - y = 1\end{array} \right.$$

A) $( - 6 , - 7 ) , ( 7,6 )$
В) $( 6,7 ) , ( 7,6 )$
C) $( 6 , - 7 ) , ( 7 , - 6 )$
D) $( - 6,7 ) , ( - 7,6 )$

Question 63

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = 8 \\x ^ { 2 } - 2 y ^ { 2 } = 12\end{array} \right.$$

A) $( \sqrt { 10 } , \sqrt { 2 } ) , ( \sqrt { 10 } , - \sqrt { 2 } )$
B) $( \sqrt { 10 } , \sqrt { 2 } ) , ( \sqrt { 10 } , - \sqrt { 2 } ) , ( - \sqrt { 10 } , \sqrt { 2 } ) , ( - \sqrt { 10 } , - \sqrt { 2 } )$
C) $( \sqrt { 10 } , \sqrt { 2 } ) , ( - \sqrt { 10 } , - \sqrt { 2 } )$
D) $\varnothing$

Question 64

Solve.
How many real solutions are possible for a system of equations whose graphs are a hyperbola and a circle?

A) $1,2,3$ , or 4 real solutions
B) $0,1,2,3$ , or 4 real solutions
C) $0,1,2$ , or 3 real solutions
D) 1,2 , or 3 real solutions

Question 65

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } + 4 y ^ { 2 } = 5 \\x - y = - 3\end{array} \right.$$

A) $( 0,0 )$
B) $\left( \frac { 3 + \sqrt { 29 } } { 5 } , \frac { - 12 + \sqrt { 29 } } { 5 } \right) , \left( \frac { 3 + \sqrt { 29 } } { 5 } , \frac { - 12 - \sqrt { 29 } } { 5 } \right) , \left( \frac { 3 - \sqrt { 29 } } { 5 } , \frac { - 12 + \sqrt { 29 } } { 5 } \right) , \left( \frac { 3 - \sqrt { 29 } } { 5 } , \frac { - 12 - \sqrt { 29 } } { 5 } \right)$
C) $\left( \frac { - 12 + \sqrt { 29 } } { 5 } , \frac { 3 + \sqrt { 29 } } { 5 } \right) , \left( \frac { - 12 + \sqrt { 29 } } { 5 } , \frac { 3 - \sqrt { 29 } } { 5 } \right) , \left( \frac { - 12 - \sqrt { 29 } } { 5 } , \frac { 3 + \sqrt { 29 } } { 5 } \right) , \left( \frac { - 12 - \sqrt { 29 } } { 5 } , \frac { 3 - \sqrt { 29 } } { 5 } \right)$
D) $\varnothing$

Question 66

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}- 48 x - y & = 14 \\x y & = 1\end{aligned} \right.$$

A) $\left( - 6 , - \frac { 1 } { 6 } \right) , \left( - 8 , - \frac { 1 } { 8 } \right)$
B) $\left( - \frac { 1 } { 6 } , - 6 \right) , \left( - \frac { 1 } { 8 } , - 8 \right)$
C) $( 6 , - 6 ) , ( 8 , - 8 )$
D) $\varnothing$

Question 67

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 1 \\x ^ { 2 } + ( y + 4 ) ^ { 2 } = 9\end{array} \right.$$

A) $( 1,0 )$
В) $( - 1,0 )$
C) $( 0,1 )$
D) $( 0 , - 1 )$

Question 68

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 81 \\y & = \frac { 1 } { 9 } x ^ { 2 } - 9\end{aligned} \right.$$

A) $( - 9,0 ) , ( 0,9 ) , ( 0 , - 9 )$
B) $( - 9,0 ) , ( 9,0 ) , ( 0 , - 9 )$
C) $( - 9,0 ) , ( 9,0 )$
D) $( - 9,0 ) , ( 9,0 ) , ( 0,9 )$

Question 69

Solve.
How many real solutions are possible for a system of equations whose graphs are a circle and a line?

A) 0,1 , or 2 real solutions
B) $0,1,2$ , or 3 real solutions
C) 0,2 , or 3 real solutions
D) 1 or 2 real solutions

Question 70

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}y & = x ^ { 2 } - - 4 \\- 8 x - y & = 8\end{aligned} \right.$$

A) $( 6,40 ) , ( 2,8 )$
B) $( - 6,40 ) , ( - 2,8 )$
C) $( - 6,32 ) , ( - 2,0 )$
D) $( 6,40 ) , ( - 2,8 )$

Question 71

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } y = x ^ { 2 } + 8 \\y = - x ^ { 2 } + 10\end{array} \right.$$

A) $( 1,9 ) , ( 1 , - 9 ) , ( - 1,9 ) , ( - 1 , - 9 )$
B) $( 9,1 ) , ( 9 , - 1 )$
C) $( 1,9 ) , ( - 1,9 )$
D) $\varnothing$

Question 72

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}y & = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } & = 5\end{aligned} \right.$$
B) $( 2 , - 1 ) , ( 1,2 ) , ( - 1,2 ) , ( - 2 , - 1 )$

A) $( 1,2 ) , ( - 1,2 )$
D) $( 2 , - 1 ) , ( - 2 , - 1 )$

Question 73

Solve.
How many real solutions are possible for a system of equations whose graphs are a parabola and a hyperbola?

A) 1,2 , or 3 real solutions
B) $1,2,3$ , or 4 real solutions
C) $0,1,2$ , or 3 real solutions
D) $0,1,2,3$ , or 4 real solutions

Question 74

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x = y ^ { 2 } - 10 \\x = y ^ { 2 } - 5 y\end{array} \right.$$

A) $( - 6 , - 2 )$
B) $( 14 , - 2 )$
C) $( - 6,2 )$
D) $( - 6 , - 2 ) , ( 14,2 )$

Question 75

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 37 \\x ^ { 2 } + y ^ { 2 } = 43\end{array} \right.$$

A) $( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
B) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } ) , ( 2 \sqrt { 10 } , - \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , - \sqrt { 3 } )$
C) $( 2 \sqrt { 10 } , \sqrt { 3 } ) , ( - 2 \sqrt { 10 } , \sqrt { 3 } )$
D) $\varnothing$

Question 76

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}y & = x + 2 \\x ^ { 2 } - y ^ { 2 } & = 4\end{aligned} \right.$$

A) $( - 2,0 ) , ( 2,0 )$
B) $( - 2,0 )$
C) $( 2,0 )$
D) $\varnothing$

Question 77

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 97 \\x ^ { 2 } - y ^ { 2 } = 65\end{array} \right.$$

A) $( 9,4 ) , ( 4,9 ) , ( - 9 , - 4 ) , ( - 4 , - 9 )$
B) $( 9 , - 4 ) , ( 9,4 )$
C) $( - 9 , - 4 ) , ( - 4 , - 9 )$
D) $( 9,4 ) , ( - 9,4 ) , ( 9 , - 4 ) , ( - 9 , - 4 )$

Question 78

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } 10 x ^ { 2 } - 5 y ^ { 2 } = 15 \\- x ^ { 2 } + y ^ { 2 } = 1\end{array} \right.$$

A) $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } ) , ( - 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$
B) $( \sqrt { 5 } , 2 ) , ( \sqrt { 5 } , - 2 ) , ( - \sqrt { 5 } , 2 ) , ( - \sqrt { 5 } , - 2 )$
C) $( 2 , \sqrt { 5 } ) , ( - 2 , - \sqrt { 5 } )$
D) $( 2 , \sqrt { 5 } ) , ( 2 , - \sqrt { 5 } )$

Question 79

Solve the nonlinear system of equations.
$$\left\{ \begin{array} { l } 10 x ^ { 2 } + y ^ { 2 } = 100 \\10 x ^ { 2 } - y ^ { 2 } = 100\end{array} \right.$$

A) $( \sqrt { 10 } , 0 ) , ( - \sqrt { 10 } , 0 )$
B) $( 0,10 ) , ( 0 , - 10 )$
C) $( 10,0 ) , ( - 10,0 )$
D) $( 0 , \sqrt { 10 } ) , ( 0 , - \sqrt { 10 } )$

Question 80

Solve the nonlinear system of equations.
$$\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 625 \\x & = y ^ { 2 } - 25\end{aligned} \right.$$

A) $( 24,7 ) , ( 24 , - 7 )$
B) $( - 25,0 ) , ( 24,49 ) , ( 24 , - 49 )$
C) $( - 25,0 ) , ( 24,7 ) , ( 24 , - 7 )$
D) $\varnothing$