What is the asymptotes of 4x^2-y^2+40x-4y+80=0 ?

The asymptotes of 4x^2-y^2+40x-4y+80=0 is y=2(x+5)-2,\quad y=-2(x+5)-2

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asymptotes of 4x^2-y^2+40x-4y+80=0

asymptotes

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0

y = 2 (x + 5) - 2, y = - 2 (x + 5) - 2

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0 :

Right-left Hyperbola with

(h, k) = (- 5, - 2), a = 2, b = 4

y = \frac{4}{2} (x - (- 5)) + (- 2), y = - \frac{4}{2} (x - (- 5)) + (- 2)

Refine

y = 2 (x + 5) - 2, y = - 2 (x + 5) - 2

x^{2} - 16 y^{2} = 16

- \frac{y ^{2}}{1} + \frac{x ^{2}}{49} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

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

What is the asymptotes of 4x^2-y^2+40x-4y+80=0 ?
The asymptotes of 4x^2-y^2+40x-4y+80=0 is y=2(x+5)-2,\quad y=-2(x+5)-2