Precalculus work...

Chapter 9 Test

Question 1 A parabola has its vertex at the origin, and the equation of its directrix is y=−10 . Find the coordinates of the focus.

a. (0,−10) b. (−10,0) c. (0,10) d. (10,0)

Question 2 A parabola has its vertex at the origin, and the coordinates of its focus are (0,10) . Find the equation of the directrix.

a. x=10 b. x=−10 c. y=10 d. y=−10

Question 3 y2=−24x Find the vertex.

a. (0, 0) b. (0, – 5) c. (0, – 20) d. (– 20, 0)

Question 4 y2=– 8x Find the focus.

a. (– 2, 0) b. (2, 0) c. (0, – 2) d. (0, 2)

Question 5 y2=– 8x Find the directrix.

a. x=– 2 b. y=– 2 c. x=2 d. y=2

Question 6 y2=– 8x Sketch the graph.

a. b. c. d.

Question 7 x2=14y Locate the directrix.

a. x=−7 /2 b. y=– 7 /2 c. x = 7 /2 d. y = 7/2

Question 8 Find the coordinates of the focus to two decimal places. x2=– 77y

a. (– 19.25, 0) b. (0, – 19.25) c. (0, 19.25) d. (– 77, 0)

Question 9 Find the equation of the parabola with vertex at the origin, axis of symmetry the x- or y-axis, and directrix y=7.

a. y2=– 28x b. y2=28x c. x2=– 28y d. x2=28y

Question 10 Find the equation of the parabola with vertex at the origin, axis of symmetry the y-axis, and passing through (8, 4).

a. y2=16x b. y2=4x c. x2=16y d. x2=4y

Question 11 Find the distance between the foci of an ellipse that has a major axis of length 20 and a minor axis of length 16.

a. 6 b. 12 c. 24 d. 18

Question 12 Find the length of the major axis of an ellipse that has the distance between the foci equal to 10 and the length of the minor axis equal to 24.

a. 13 b. 18 c. 52 d. 26

Question 13 9x2+y2=36 Sketch the graph.

a. b. c. d,

Question 14 25x2+y2=100 Find the lengths of the major and minor axes.

a. Major axis length = 10, minor axis length = 2 b. Major axis length = 20, minor axis length = 2 c. Major axis length = 10, minor axis length = 4 d. Major axis length = 20, minor axis length = 4

Question 15 Find the equation of an ellipse in the form x2

M +

y2

N =1 , M, N>0 with major axis

along the x-axis, major axis length 16 and minor axis length 14.

a. x2

8 +

y2

7 =1 b.

x2

7 +

y2

8 =1 c.

x2

64 +

y2

49 =1 d.

x2

49 +

y2

64 =1

Question 16 A landscaper wishes to create an elliptical garden 12 m long and 4 m across with decorative fountains located at the foci. How far apart are the fountains?

a. 13.42 m b. 11.38 m c. 16.10 m d. 16.58 m

Question 17 y2 – 4x2=16 Sketch the graph.

a. b. c. d.

Question 18 y2 – 4x2=16 Find the coordinates of the foci.

a. b.

c. d.

Question 19 Find an equation of a hyperbola in the form x2

M −

y2

N =1 or y

2

N −

x2

M =1 , M , N>0

whose center is at the origin and whose graph is shown .

a. y2

4 −x2=1 b.

x2

4 −y2=1 c. y2−

x2

4 =1 d. x2−

y2

4 =1

Question 20 Find an equation of a hyperbola in the form x2

M −

y2

N =1 or y

2

N −

x2

M =1 , M , N>0

whose center is at the origin, whose transverse axis is on the y-axis and has length 12, and whose foci are a distance of 7 units from the center.

a. y2

13 −

x2

36 =1 b.

x2

13 −

y2

36 =1 c.

y2

36 −

x2

13 =1 d.

x2

36 −

y2

13 =1

Question 21 Find the equations of the asymptotes. 25x2 – 9y2=225

a. y=± 5 3

x b. y=± 3 5

x c. y=± 25 9

x d. y=± 9

25 x

Question 22 Find the coordinates of the foci 25x2+9y2+150x+54y+81=0

a. (1, – 3),(– 7, – 3) b. (– 3, 1) ,( – 3, – 7) c. (7, 3),(– 1, 3) d. (3, 7) ,(3, 7)