1. From equations to graphs
Ellipses
From equations to graphs

2. 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

3. 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

4. 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.

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

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