Find the asymptotes of the hyperbola 4x2 y2 32x 12y 72

Find the asymptotes of the hyperbola.

4x² - y² - 32x - 12y - 72 = 0

y + 4 = - 2(x - 6) and y + 4 = 2(x - 6)

Solution

4x²-y²-32x-12y-72=0

4(x²-8x+16-16) -(y²+12y+36-36)-72=0

4(x-4)²-(y+6)²=72+64-36

(x-4)²/25 -(y+6)²/100=1

a=5,b=10

h=4 ,k=-6

Asymptote,y=+-(10/5)(x-4)-6

y+6=2(x-4) , y+6=-2(x-4)