6-4 Hyperbolas

This week we learned section 6-4. Section 6-4 was dealing with hyperbolas

Hyperbolas are in the form x^2/a^2 –y^2/b^2 or –x^2/a^2 + y^2/b^2.

Part of the Equation:
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-negative denominator
4. Length of minor –2 square root of smaller denominator
5. Vertex – square root of non-negative 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)
8.Asymptotes –
If x is major: y = +/- b/ax
If y is major: y = +/- a/bx


Examples:

X^2?25-Y^2/100=1

1. x
2. y
3. 10
4. 20
5. (5,0)(-5,0)
6. (0,10)(0,-10)
7. (5square root of 5,0)( -5square root of 5,0)
8. y= + and – 2x


Basically if you know your rules and stuff it easy and it the same thing as 6-3 rules but couple new steps to 6-4 that all.