# Math Help - Hyperbola

1. ## Hyperbola

Can you guys help me illustrate the transverse axis, a, b , vertices, directrix, latus rectum, etc. of this hyperbola
$16x^2 - 9y^2 - 64x - 18y - 89 = 0$

with standard equation of (x-2)^2 over 9 - (y+1)^2 over 16 = 1

Thanks!

2. Originally Posted by reiward
Can you guys help me illustrate this hyperbola
$16x^2 - 9y^2 - 64x - 18y - 89 = 0$

with standard equation of (x-2)^2 over 9 - (y+1)^2 over 16 = 1
Rewrite the equation as
$16x^2 - 64x +a^2 - 9y^2 - 18y + b^2 = 89 + a^2 + b^2 + 1$
You have to find the value of a and b such that
$16(x - a)^2 - 9(y - b)^2 = 90 + a^2 + b^2$
Now rearrange the terms to get the required result.