6-3

6-3 Ellipses
This past week we learned about conics, ellipses, and hyperbolas.
Ellipses are in the form: x^2/a + y^2/b

Parts of the equation:
1. Major axis – variable with larger denominator
2. Minor axis – variable with smaller denominator
3. Length of major – 2*square root of larger denominator
4. Length of minor – 2*square root of smaller denominator
5. Vertex – square root of larger denominator
If x is major: (_,0) and (-_, 0)
If y is major: (0,_) and (0, -_)
6. Other intercepts – square root of smaller denominator … ( , ) opposite of vertex
7. Focus – smaller denominator = larger denominator – focus squared
If x is major: (0, focus)
If y is major: (focus, 0)

EXAMPLE 1: Find all the parts of x^2/9 + y^2/25.
1. y
2. x
3. 2 * the square root of 25 = 10
4. 2 * the square root of 9 = 6
5. Since y is the major, (0,5) and (0,-5)
6. (3,0) and (-3,0) 7. 9 = 25 – focus squared
focus = +/- 4 therefore, (0,4) and (0,-4) is your focus.