Circles and Parabolas Dr. Shildneck Fall, 2014

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

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

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

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

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.