Conic Sections, Course Quiz

A plane cuts a double cone at right angles to its axis (not through the vertex). The section is

A a hyperbola

B a circle

C an ellipse

D a parabola

Find the equation of the circle with centre

(1, -2)

and radius

3

.

A

x^2 + y^2 - 2x + 4y - 4 = 0

B

x^2 + y^2 + 2x - 4y - 4 = 0

C

x^2 + y^2 - 2x + 4y - 9 = 0

D

x^2 + y^2 - 2x + 4y + 4 = 0

What is the radius of

x^2 + y^2 + 2x - 4y - 4 = 0

?

A

2

B

\sqrt{5}

C

3

D

9

Which way does the parabola

y^2 = -8x

open?

A To the right

B To the left

C Upward

D Downward

Find the focus of

x^2 = 12y

.

A

(0, -3)

B

(0, 12)

C

(3, 0)

D

(0, 3)

A parabola has vertex at the origin, axis along the

x

-axis and passes through

(2, 4)

. Find its equation.

A

y^2 = 8x

B

y^2 = 16x

C

y^2 = 2x

D

x^2 = 8y

An ellipse has vertices

(\pm 10, 0)

and foci

(\pm 6, 0)

. Find

b^2

.

A

16

B

136

C

4

D

64

For every ellipse, the eccentricity

e

satisfies

A

e < 0

B

e = 1

C

e > 1

D

0 \le e < 1

Find the foci of the hyperbola

\displaystyle \dfrac{x^2}{16} - \dfrac{y^2}{9} = 1

.

A

(\pm 5, 0)

B

(\pm 4, 0)

C

(0, \pm 5)

D

(\pm \sqrt{7}, 0)

What is the length of the latus rectum of

y^2 = 12x

?

A

6

B

48

C

12

D

3

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