What is the asymptotes of 4x^2-8x-9y^2-72y+112=0 ?

The asymptotes of 4x^2-8x-9y^2-72y+112=0 is y=(2(x-1))/3-4,\quad y=-(2(x-1))/3-4

Popular >

asymptotes of 4x^2-8x-9y^2-72y+112=0

asymptotes

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0

y = \frac{2 ( x - 1 )}{3} - 4, y = - \frac{2 ( x - 1 )}{3} - 4

Solution steps

y = \pm \frac{a}{b} (x - h) + k

Calculate Hyperbola properties

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 4), a = 27, b = 37

y = \frac{2 7}{3 7} (x - 1) + (- 4), y = - \frac{2 7}{3 7} (x - 1) + (- 4)

Refine

y = \frac{2 ( x - 1 )}{3} - 4, y = - \frac{2 ( x - 1 )}{3} - 4

9 x^{2} - 25 y^{2} = 225

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{1} - \frac{( y - 1 ) ^{2}}{4} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{3} = 1

What is the asymptotes of 4x^2-8x-9y^2-72y+112=0 ?
The asymptotes of 4x^2-8x-9y^2-72y+112=0 is y=(2(x-1))/3-4,\quad y=-(2(x-1))/3-4