School & Chat

Posted: **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

$y = k \pm \frac{b}{a}(x-h)$

$y = k \pm \frac{a}{b}(x-h)$

Transverse axis is horizontal

Transverse axis is vertical

School & Chat

Hyperbolas

Hyperbolas