hyperbolas?

Question

do asymptotes always start at the center of the hyperbola? if the center was (1,3) and the asymptote 5/3 or something, would their crossing be the center?

can the B value be higher that the A value when the graph is going left and right?

thanks in advance for any help

Answer 1

A hyperbola with center at (h,k) has the equation:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1 if transverse axis is || to OX.
(y-k)^2/a^2- (x-h)^2/b^2 =1 if transverse axis || to OY.

Yes, the asymptotes always go through the center(h,k) of the hyperbola. If a=b, we have a rectangular or equilateral hyperbola, and the asymptotes are perpendicular.

b= sqrt(c^2-a^2) where c always > a.
Yes it is possible for b>a. x^2-4-y@/16 +1 is an example.

This affects the asymptotes which are +/- bx/a, and
.