What is the asymptotes of x^2-4y^2-10x-8y-4=0 ?

The asymptotes of x^2-4y^2-10x-8y-4=0 is y=(x-5)/2-1,\quad y=-(x-5)/2-1

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asymptotes of x^2-4y^2-10x-8y-4=0

asymptotes

x^{2} - 4 y^{2} - 10 x - 8 y - 4 = 0

y = \frac{x - 5}{2} - 1, y = - \frac{x - 5}{2} - 1

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} - 10 x - 8 y - 4 = 0 :

Right-left Hyperbola with

(h, k) = (5, - 1), a = 5, b = \frac{5}{2}

y = \frac{\frac{5}{2}}{5} (x - 5) + (- 1), y = - \frac{\frac{5}{2}}{5} (x - 5) + (- 1)

Refine

y = \frac{x - 5}{2} - 1, y = - \frac{x - 5}{2} - 1

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 + 5 = 0

\frac{( y - 2 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{4} = 1

(x - 1)^{2} - (y + 2)^{2} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{64} = 1

What is the asymptotes of x^2-4y^2-10x-8y-4=0 ?
The asymptotes of x^2-4y^2-10x-8y-4=0 is y=(x-5)/2-1,\quad y=-(x-5)/2-1