What is the asymptotes of 4x^2-y^2-8x+6y-4=0 ?

The asymptotes of 4x^2-y^2-8x+6y-4=0 is y=2(x-1)+3,\quad y=-2(x-1)+3

Popular >

asymptotes of 4x^2-y^2-8x+6y-4=0

asymptotes

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

y = 2 (x - 1) + 3, y = - 2 (x - 1) + 3

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0 :

Up-down Hyperbola with

(h, k) = (1, 3), a = 1, b = \frac{1}{2}

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

Refine

y = 2 (x - 1) + 3, y = - 2 (x - 1) + 3

4 y^{2} - 25 x^{2} = 100

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

\frac{( y - 2 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{1} = 1

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

25 y^{2} - 36 (x - 8)^{2} = 900

What is the asymptotes of 4x^2-y^2-8x+6y-4=0 ?
The asymptotes of 4x^2-y^2-8x+6y-4=0 is y=2(x-1)+3,\quad y=-2(x-1)+3