1. Circles and Parabolas
Dr. Shildneck
Fall, 2014

2. Circles
Standard Equation (x-h)2 + (y-k)2 = r2 h = x-coordinate of the center k = y-coordinate of the center r = radius of the circle

3. Example (x+4)2 + (y-2)2 = 25 Quick Graphs Find and Plot Center
Find Radius
Plot points to the top, bottom, right and left of center.
Sketch a circle through those four points.
Example
(x+4)2 + (y-2)2 = 25

4. Parabolas
Standard Equations (x-h)2 = 4p(y-k) (y-k)2 = 4p(x-h) h = x-coordinate of the vertex k = y-coordinate of the vertex p = distance from the vertex to the focus -p = distance from the vertex to the directrix 4p = distance across the parabola through the focus
If the x-term is squared, the parabola opens vertically
If the y-term is squared, the parabola opens horizontally

5. Example 8(x+7) = (y-2)2 Quick Graphs Find and Plot Vertex
Determine the orientation
Find p and plot the focus
Graph the directrix
Find 4p and find each point (2p) from the focus.
Example
8(x+7) = (y-2)2

6. Writing Equations Know the standard form of the equations
Sketch the curve described
Find the critical values needed for the equation
Plug into the equation.