# Unit 11: Chapter 18 - Circles and Parabolas

## Circles

Definition: The set of all points in a plane equal distance from a fixed point called the center.

General form: Ax2 + Cy2 + Dx + Ey + F = 0

Standard form: (x - h)2 + (y - k)2 = r2

center: (h, k)

### Testing if a point is on, inside, or outside a circle

#### using the equation of a circle:

1. plug in the point in question
2. compare to r2...
• = means on the circle
• > means outside the circle
• > means inside the circle

### Finding Symmetric Points

Use the lines x = h and y = k as lines of symmetry. (remember that vertex is (h, k)

## Parabolas

Definition: The set of all points in a plane equal distance from a fixed point called the focus and a fixed line called the directrix.

p is the distance (with direction) between the vertex and the focus or opposite the directrix
p = 14a

General formVertex form
 Ax2 + Dx + Ey + F = 0 Cy2 + Dx + Ey + F = 0 y = a(x - h)2 + k x = a(y - k)2 + h vertex: (h, k) vertex: (h, k) *watch out (remember to reverse k and h for horizontal parabola's vertex)

In circles, A = C, and both are not equal to 0. In parabolas, A = 0 or C = 0.