Hyperbolas

Welcome
Please register to have access to more features! It is highly recommended that you have Javascript enabled; many features will not work unless you do. The recommended browsers are Firefox and Chrome; the board is also NOT mobile-friendly. Please invite your friends! If you were referred by someone (ex. me, Jessica) please put their username in the referral box on the registration page. Ask them if you don't know their username. If you are visiting for TESTING PURPOSES ONLY, this is the test account information: Username: Test Password: test123

Welcome

Please register to have access to more features!

It is highly recommended that you have Javascript enabled; many features will not work unless you do. The recommended browsers are Firefox and Chrome; the board is also NOT mobile-friendly.

Please invite your friends!

If you were referred by someone (ex. me, Jessica) please put their username in the referral box on the registration page. Ask them if you don't know their username.

If you are visiting for TESTING PURPOSES ONLY, this is the test account information:

Username: Test
Password: test123

Hyperbolas

Looking for a topic?
View the Math Topics Directory to find topics quicker under different kinds of math.

Followers: 0
Favorites: 0
Views: 2069

Reply with quote

Hyperbolas

Post Number: #1 by Jessica » May 4th, 2011, 4:11 pm

A hyperbola is the set of all points (x, y) in a plane, the DIFFERENCE of whose distances from two distinct fixed points (foci) is a positive constant.

Standard equation

Center (h, k)

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

$\frac{(x-h)^2}{b^2}-\frac{(y-k)^2}{a^2}=1$

Transverse axis is horizontal (faces left, right)

Transverse axis is vertical (faces up, down)

If x² is FIRST, the major axis is horizontal.
If y² is FIRST, the major axis is vertical.
The FIRST denominator is ALWAYS a²

The vertices are a units from the center, and the foci are c units from the center, with $c^2=a^2+b^2$

ASYMPTOTES OF A HYPERBOLA