Welcome

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.

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:

Test

Select a forum to post in:

## Hyperbolas

Math topics

Moderators: Jessica, Teachers

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

### Hyperbolas

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

 $y = k \pm \frac{b}{a}(x-h)$$y = k \pm \frac{a}{b}(x-h)$ Transverse axis is horizontalTransverse axis is vertical
• 0

Tales of Ostlea :
Dragon Cave :
Magistream :

Jessica
Board Owner
Topic Author

Sapphire

Posts: 3,470
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm