What is the asymptotes of x^2-4y^2-2x+16y=20 ?

The asymptotes of x^2-4y^2-2x+16y=20 is y=(x-1)/2+2,\quad y=-(x-1)/2+2

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asymptotes of x^2-4y^2-2x+16y=20

asymptotes

x^{2} - 4 y^{2} - 2 x + 16 y = 20

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} - 2 x + 16 y = 20 :

Right-left Hyperbola with

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

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

Refine

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

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

x^{2} - y^{2} < 1

\frac{( x + 5 ) ^{2}}{4} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{16} = 1

2 x^{2} - 2 y^{2} - 20 x + 16 y + 16 = 0

What is the asymptotes of x^2-4y^2-2x+16y=20 ?
The asymptotes of x^2-4y^2-2x+16y=20 is y=(x-1)/2+2,\quad y=-(x-1)/2+2