What is the asymptotes of 25x^2-16y^2+50x-32y-391=0 ?

The asymptotes of 25x^2-16y^2+50x-32y-391=0 is y= 5/4 (x+1)-1,\quad y=-5/4 (x+1)-1

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asymptotes of 25x^2-16y^2+50x-32y-391=0

asymptotes

25 x^{2} - 16 y^{2} + 50 x - 32 y - 391 = 0

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

Solution steps

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

Calculate Hyperbola properties

25 x^{2} - 16 y^{2} + 50 x - 32 y - 391 = 0 :

Right-left Hyperbola with

(h, k) = (- 1, - 1), a = 4, b = 5

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

Refine

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

\frac{( y ) ^{2}}{12} - \frac{x ^{2}}{16} = 1

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

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

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

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

What is the asymptotes of 25x^2-16y^2+50x-32y-391=0 ?
The asymptotes of 25x^2-16y^2+50x-32y-391=0 is y= 5/4 (x+1)-1,\quad y=-5/4 (x+1)-1