You may want to review equations of ellipses first.

Equations of hyperbolas look like −4*x*^{2}
+ *y*^{2} − 16 = 0. (Note that one of the
coefficients is negative; that's what makes it a hyperbola instead
of an ellipse.) As with ellipses, we'll start with hyperbolas
centered at the origin. Also just like ellipses, we start by
dividing both sides by 16, so it becomes
−1 ⁄ 4 * *x*^{2} +
1 ⁄ 16 * *y*^{2} − 1. The
minus sign is in front of the *x*^{2} term, so the
hyperbola is horizontal. (What a hyperbola looks like is hard to
describe; ideally your teacher will draw you a pictures of both a
horizontal and a vertical hyperbola.) So then we look at
the *y*^{2} term to find the radius, which comes out
to 16, the square root of 4. (If it were vertical, then we'd get
the radius from the *x*^{2} term. Also, on this site,
there's a check box for horizontal. If it's vertical, then just
leave it unchecked.)

Unlike ellipses, hyperbolas have only one radius. They do,
however, have something that I'll call the asymptotic slope. (To
see what this means geometrically, you'll want to look at a
picture.) To find it, divide the coefficient
of *x*^{2} by the coefficient
of *y*^{2}, ignoring signs. Here, that means you get
4 / 1 = 4. Then, you take the square root, getting 2, the
answer.