Question 1

Given the equation $$4p = -8$$ for a parabola, what is the value of $$p$$ and what does this tell you about the direction the parabola opens?

Accepted Answer

$$p = -2$$, parabola opens down

Question 2

What is the equation of the directrix for a parabola with vertex at $$(1, -5)$$ and $$p = -2$$?

Accepted Answer

$$y = -3$$

Question 3

A parabola has its vertex at $$(3, -4)$$ and opens to the right. If $$4p = 16$$, what is the equation of its directrix?

Accepted Answer

$$x = -1$$

Question 4

Given the ellipse $$\$$\frac{$$(x-2)^2$$}{7} + \frac{$$(y-2)^2$$}{12} = 1\$$ with center (2$$,2)$, what are the coordinates of the foci?

Accepted Answer

$$(2, 2 \pm \sqrt{5})$$

Question 5

What is the standard form equation for a hyperbola centered at $$(0, -1)$$ opening up and down with $$a^2 = 2$ and b^2$ = 9$$?

Accepted Answer

$$\frac{(y+1)^2$}{9} - \frac{x^2$}{2} = 1$$

Question 6

For the ellipse $$\$$\frac{$$(x-2)^2$$}{7} + \frac{$$(y-2)^2$$}{12} = 1\$, what is the length of the major axis?

Accepted Answer

$$2	imes 2\sqrt{3}$$

Question 7

Given the hyperbola $$\$$\frac{$$x^2$$}{2} - \frac{$$(y+1)^2$$}{9} = 1\$, what are the equations of its asymptotes?

Accepted Answer

$$y = \pm \frac{3}{\sqrt{2}}x - 1$$

Question 8

Which of the following equations represents a parabola opening to the left?

Accepted Answer

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

Question 9

If the equation $$12(x-2)^2$$ + $$7(y-2)^2 = 84$ is given, what type of conic section does it represent and what is its standard form?

Accepted Answer

Ellipse, $$\frac{(x-2)^2$}{7} + \frac{(y-2)^2$}{12} = 1$$

Question 10

Given the standard form for a hyperbola $$\$$\frac{$$(x-h)^2$$}{$$a^2$$} - \frac{$$(y-k)^2$$}{$$b^2$$} = 1\$, what is the distance between the center and each focus?

Accepted Answer

$$c = \sqrt{a^2$ + b^2$}$$

Question 11

A parabola has vertex at $$(1, -5)$$ and focus at $$(1, -7). $$What is the equation of the parabola in standard form?

Accepted Answer

$$(x-1)^2 = -8(y+5$$)$$

Question 12

For the ellipse $$\$$\frac{$$(x-2)^2$$}{7} + \frac{$$(y-2)^2$$}{12} = 1\$$, what is the value of c$ (distance from center to focus)?

Accepted Answer

$$c = \sqrt{12 - 7}$$

Question 13

Which of the following is the standard form for a parabola opening up with vertex $$(h, k)$$?

Accepted Answer

$$4p(y-k) = (x-h)^2$

Question 14

Given the hyperbola $$\$$\frac{$$x^2$$}{2} - \frac{$$(y+1)^2$$}{9} = 1\$, what are the coordinates of the vertices?

Accepted Answer

$$(\pm \sqrt{2}, -1)$$

Question 15

Which conic section is represented by the equation $$\$$\frac{$$(x-h)^2$$}{$$a^2$$} + \frac{$$(y-k)^2$$}{$$b^2$$} = 1\$?

Accepted Answer

Ellipse

Question 16

If a hyperbola has the equation $$\$$\frac{$$x^2$$}{2} - \frac{$$(y+1)^2$$}{9} = 1\$, what is the distance between the foci?

Accepted Answer

$$2\sqrt{11}$$

Question 17

Which of the following is the standard form for a hyperbola opening left and right?

Accepted Answer

$$\frac{(x-h)^2$}{a^2$} - \frac{(y-k)^2$}{b^2$} = 1$$

Question 18

Given the ellipse $$\$$\frac{$$(x-2)^2$$}{7} + \frac{$$(y-2)^2$$}{12} = 1\$$, what are the x$-intercepts?

Accepted Answer

$$(2 \pm \sqrt{7}, 2)$$

Question 19

A parabola has vertex at $$(3, -4)$$ and $$p = 4. $$What is the equation of the focus?

Accepted Answer

$$(7, -4)$$

Precalculus Study Guide: Conics (Parabolas, Ellipses, Hyperbolas)

Study Guide - Practice Questions

Study Guide - Flashcards