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)
radius: r

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...

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 = 1⁄4a

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.