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Unit 8 Mr. Kuhtz Review

Total questions: 20

Worksheet time: 40mins

Name
Class
Date
1.

What type of equation is shown? 7x2+3y2=5

a)

Ellipse

b)

Hyperbola

c)

Quadratic

d)

Circle

2.

Find the foci of x2/64+y2/9=1

a)

(8.544,0) (-8.544,0)

b)

(0,8.544) (0,-8.544)

c)

(7.416,0) (-7.416,0)

d)

(0,7.416) (0,-7.416)

3.

Which graph represents the equation x2/4+y2/25=1?

a)
b)
c)
d)
4.

Find the standard equation of the ellipse with vertices at (5,1) and (-3,1) and passes through the point (1,3)

a)

(x-1)2/16-(y-1)2/4=1

b)

(x-5)2/4+(y-1)2=1

c)

(x-1)2/16+(y-1)2/4=1

d)

(x-1)2/162+(y-1)2/42=1

5.

Find the center of the ellipse (x+6)2/81+(y-1)2/212=1

a)

(-6,1)

b)

(6,-1)

c)

(9, √212)

d)

(-9, √212)

6.

Find the foci of the equation (x+2)2/9+(y-1)2/25=1

a)

[ (-2, 5) (-2, -3)]

b)

[(-2,1) (2,1)]

c)

[(-2,3) (2,1)]

d)

[(1,-2) (1,2)]

7.

Identify the conic section 4x2-y2+8x+2y=0

a)

Hyperbola

b)

Quadratic

c)

Circle

d)

Ellipse

8.

Find the standard equation of the hyperbola with vertices (+/- 8,0) and an asymptote y=+/- 2x

a)

x2/64+y2/96= 1

b)

y2/256-x2/64= 1

c)

x2/64-y2/256= 1

d)

y2/64-x2/256= 1

9.

What is the standard equation of a hyperbola centered at its origin with vertices at (+/-√4, 0) and a foci at (+/- √7,0)?

a)

x2/7-y2/3= 1

b)

x2/4-y2/3= 1

c)

x2/7+y2/3= 1

d)

x2/3-y2/4= 1

10.

Find the standard equation of the hyperbola centered at the origin with y intercepts at +/- 8 asymptotes y=+/- 4/3x.

a)

y2/64-x2/36 = 1

b)

y2/36-x2/64 = 1

c)

y2/64-x2/9 = 1

d)

y2/64+x2/9 = 1

11.

Find the vertices of the hyperbola and the slopes of the asymptotes from this equation: x2/4- (y+2)2/9=1

a)

(2,-2) and (-2,-2), +/- 3/2

b)

(2,-2) and (-2,-2) +/-2/3

c)

(-2,2) and (-2,-2)+/-2/3

d)

(-2,2) and (-2,-2) +/- 3/2

12.

Find the equation of the parabola with focus at (-5,0) and a directrix at x=5

a)

y2=-20x

b)

y2=-5x

c)

x2=-20y

d)

-5y2=y

13.

Find the directrix and focus of the parabola -y2=8x.

a)

[x=2, (-2,0)]

b)

[x=4, (-4,0)]

c)

[x=-2, (2,0)]

d)

[y=4, (0,4)]

14.

Find the equation for the parabola with a vertex at the origin and a foci of (3,0).

a)

(x-3)2=(y+4)

b)

y2=12x

c)

x2=9x

d)

y2=9x

15.

What is the vertex of this equation? (y-9)2=8(x+13)

a)

(9,-13)

b)

(-13,9)

c)

(9,-104)

d)

(-104,9)

16.

Find the standard equation of the conic section and identify the type of conic section: 2y-2x2+12x-10=0

a)

(x-6)2 = (y+5)

b)

(x-4)2 = (y+3)

c)

(x+6)2 = (y-5)

d)

(x-3)2 = (y+4)

17.

Find the directrix of the equation (x+3)2 = -2y+4

a)

x = 1/2

b)

y = 3/2

c)

x = -3/4

d)

y = -1/2

18.

A student wants to learn about how parabolic flashlights work. They figure out that the reflector is 6 inches wide and 3 inch deep. If the filament is at the focus, how far away is the filament from the vertex of the parabola created?

a)

3/4 in

b)

1/2 in

c)

1/4 in

d)

5/4 in

19.

Two families go to a restaurant with a ceiling shaped like a semi-ellipse. The Johnson Family sat at the foci at the right side room and the Smith Family sat at the other foci. The room is 30 ft wide and a wall height of 6 ft. The highest point of the ceiling is 12 ft tall. How far apart are the two tables?

a)

29 ft

b)

24.5 ft

c)

27.5 ft

d)

29.5 ft

20.

Sally has a 10 in by 10 in piece of yellow paper and cuts a circle from this paper. If the circle cut out has a radius of 5 in, assuming the center is at the origin, what is the standard equation of the circle?

a)

x2+y2 = 100

b)

x2+y2 = 25

c)

x2/5 + y2/10 = 1

d)

x2/10 + y2/5 = 1