What is the asymptotes of-16x^2+25y^2-64x-150y-239=0 ?

The asymptotes of-16x^2+25y^2-64x-150y-239=0 is y= 4/5 (x+2)+3,\quad y=-4/5 (x+2)+3

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asymptotes of-16x^2+25y^2-64x-150y-239=0

asymptotes

- 16 x^{2} + 25 y^{2} - 64 x - 150 y - 239 = 0

y = \frac{4}{5} (x + 2) + 3, y = - \frac{4}{5} (x + 2) + 3

Solution steps

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

Calculate Hyperbola properties

- 16 x^{2} + 25 y^{2} - 64 x - 150 y - 239 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 3), a = 4, b = 5

y = \frac{4}{5} (x - (- 2)) + 3, y = - \frac{4}{5} (x - (- 2)) + 3

Refine

y = \frac{4}{5} (x + 2) + 3, y = - \frac{4}{5} (x + 2) + 3

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

9 x^{2} - 36 y^{2} = 324

9 x^{2} - y^{2} = 36

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

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

What is the asymptotes of-16x^2+25y^2-64x-150y-239=0 ?
The asymptotes of-16x^2+25y^2-64x-150y-239=0 is y= 4/5 (x+2)+3,\quad y=-4/5 (x+2)+3