Find the asymptotes of (( x − 5 )^2)/16 − (( y + 2 )^2)/9 = 1

Question

Should be in the format y + (something) = +- (frac)(x + something) I keep getting an answer not listed, so I would love to see the process, thanks in advance!

Answer 1

Hello Chris,

The asymptotes for a hyperbola should be in the form:

y - k = ± (b/a)* (x-h) where: (h,k) are the coordinates of the center of the hyperbola

For a hyperbola, a is always the square root of the number under the (x-h)^2 parameter

b is always the square root of the number under the (y-k)^2 parameter

That means: a = sqrt(16) = 4; b = sqrt(9) = 3; and the coordinates of the center of the hyperbola whose equation you listed are (5,-2) where h = 5 and k = -2

You can now plug k, b, a and h in the equation I wrote earlier and you will get the right answer.

Cheers.