6-4

Prom is this weekend, tonight actually and I’m stressin’ big time! So this might be a little short..
Section 6-4 dealt with hyperbolas. Hyperbolas are in the form x^2/a^2 –y^2/b^2 or –x^2/a^2 + y^2/b^2.
Parts of the equation are similar to the ellipse.
1. Major axis – variable with larger denominator (non-negative)
2. Minor axis – variable with smaller denominator
3. Length of major – 2*square root of non-neg denominator
4. Length of minor – 2*square root of smaller denominator
5. Vertex – square root of non-neg 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 – focus squared = larger denominator + smaller denominator
If x is major: (focus, 0)
If y is major: (0, focus)
**SOMETHING DIFFERENT: Asymptotes –
If x is major: y = +/- b/ax
If y is major: y = +/- a/bx

EXAMPLE 1: x^2/9 – y^2/16 Find all parts.
1. x (since 16 is negative)
2. y
3. 2*square root of 9 = 6
4. 2*square root of 16 = 8
5. square root of 9 = (3, 0) and (-3,0)
6. square root of 16 = (0,4) and (0,-4)
7. 9 + 16 = 25
focus = 5
8. y = +/- 4/3x

Hope everyone has a fun, memorable weekend!