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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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