Hyperbolas

This week in Adv. Math 1^st hour we learned all about conics. There 4 types of conics: Circles, Parabolas, Hyperbolas, and Ellipses. The conic that I am going to talk about is a hyperbola. Hyperbolas and Ellipses have the same standard form but are different in the way that hyperbolas include a negative sign in its form and an ellipse does not. The standard form for a hyperbola is:

x^2 / a^2 – y^2 / b^2 = 1, or, -x^2 / a^2 + y^2 / b^2 = 1.

Steps :

1. The major axis/largest deno. is the variable that is positive.

2. The minor axis/smallest deno. is the variable that is negative.

3. The vertex is the square root of the largest deno. (put in point form.)

4. The other value is the square root of the smallest deno. (ignore the negative; put in pt. form.)

5. To find the focus, use one of these 2 formulas:

F^2= largest deno. + smallest deno. or F^2= v^2 + other value^2

6. To find horizontal asymptotes use: y= square root of y deno. / square root of x deno. * X

Example Problem:

-X^2 / 144 + Y^2 / 16 = 1

1. Y is major axis ( it is positive)

2. X is minor (it is negative)

3. Square root of 16 (major axis) = +/- 4 (0,4) (0,-4)

4. Square root of 144 (minor axis) = +/- 12 (12,0) (-12,0)

5. F^2= largest deno. + smallest deno.

F^2 = 16 + 144= 160. f^2=160. Square root both, f= square root of 160. (0, Square root of 160)

6. Y= square root of 16 / square root of 144. = 4/12 = 1/3. Y= +/- 1/3x.