From equations to graphs Ellipses From equations to graphs

The Equations What are they? Where (h, k) is…? a = ? b = ? (h, k) is the center a is the distance from the center to the longer side b is the distance from the center to the shorter side

Making it look like that equation What if I have the following: 10x2 + 2y2 = 40 What do we do to put this in the standard form of the equation? Well, it needs to be equal to 1 So divide by 40

From the equation to the graph: First find the center (h, k). Then determine a and b. Use a and b to find c. c2 = a2 – b2 Find the Focii at (h, k + c) and (h, k – c) Reminder: this is for a vertical ellipse; for horizontal ellipses the h gets the c added/subtracted. Plot everything you have.

Example From the previous example: Center? (0, 0) a = √(20) b = 2

Example (cont.) c = √(20 – 4) = √(16) = 4 Focii: (0, 0 + 4) = (0, 4) (0, 0 – 4) = (0, -4) Then we graph it