Practice Test Chapter 7 Conic Sections
Circle with center at (h,k): (x-h)^2 + (y-k)^2 = r^2
Parabolas with vertex at (h,k): Axis of Symmetry
Parallel to a Coordinate Axis , a>0
| vertex |
focus |
directrix |
equation |
description |
| (h,k) |
(h + a,k) |
x = h - a |
(y-k)^2 = 4a(x-h) |
parabola , axis of symmetry parallel
to x-axis, opens to right |
| (h,k) |
(h - a,k) |
x = h + a |
(y-k)^2 = -4a(x-h) |
parabola, axis of symmetry parallel
to x-axis, opens to left |
| (h,k) |
(h,k + a) |
y = k - a |
(x-h)^2= 4a(y-k) |
parabola, axis of symmetry parallel
to y-axis, opens up |
| (h,k) |
(h,k - a) |
y = k + a |
(x-h)^2 = -4a(y-k) |
parabola, axis of symmetry parallel
to y-axis, opens down |
Ellipses with Center at (h,k) and Major Axis Parallel
to a Coordinate Axis
| Center |
Major Axis |
Foci |
Vertices |
Equation |
| (h,k) |
Parallel to x-axis |
(h + c,k) |
(h + a,k) |
 |
| |
|
(h - c,k) |
(h - a,k) |
| (h,k) |
Parallel to y-axis |
(h,k + c) |
(h,k + a) |
 |
| |
|
(h,k - c) |
(h,k - a) |
Hyperbolas with Center at (h,k) and Transverse Axis
Parallel to a Coordinate Axis
| Center |
Transverse
Axis |
Foci |
Vertices |
Equation |
Asymptotes |
| (h,k) |
Parallel to
x-axis |
(h ± c,k) |
(h ± a,k) |
 |
 |
| (h,k) |
Parallel to
y-axis |
(h,k ± c) |
(h,k ± a) |
 |
 |
1. Match the following graphs with the correct equation.
2. Match the following graphs with the correct equation.
3. Match the following graphs with the correct equation.
4. Match the following graphs with the correct equation.
5. Complete the square for the following quadratic.
6. Find the vertex , focus, and equation for the directrix
for the following parabola.
7. Where is the center of the following circle, and what
is its radius.
8. Find the foci for the following ellipse .
9. A circle is centered at (3,4) with a radius of 5. What
is the equation of the circle?
10. A parabola has its vertex at (1,2) and its focus is at
(3,2). What is the equation of the
parabola?
11. The equation of an ellipse is:
What is the value of the semimajor axis?
What is the value of the semiminor axis? Where does the ellipse cross the
y-axis?
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