Expert: Sherry Wallin - 8/7/2009

Question
What is the center, foci, and asymptotes of the hyperbola x^2-y^2=18

Answer
Samantha~
   The center is (0,0) because there is no x or y term only squared terms. [The general form of a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 -(x-h)^2/b^2 = 1  and here you have  (x-0)^2/(3*sqrt2)^2 - (y-0)^2/(3*sqrt2)^2 = 1 and the center is (h,k) = (0,0)] The asymptotes are y =(+/-b/a)x which means one asymptote is y = x [y = (3*sqrt2/3*sqrt2)x] and the other is y = -x [y = (-3*sqrt2/3*sqrt2)x].
Note 3*sqrt2 = sqrt(18).
Foci are (h+/-c,k)[since this equation starts with positive x^2] where c^2 = b^2 + a^2 and in your case c^2 = 18 + 18 or c = sqrt(36) = 6, thus your foci are: (0,6) and (0,-6).

In the future it would be helpful if you would tell me what you already know or don't know/

Math Prof