What is the asymptotes of 4x^2-24x-25y^2+250y-489=0 ?

The asymptotes of 4x^2-24x-25y^2+250y-489=0 is y= 2/5 (x-3)+5,\quad y=-2/5 (x-3)+5

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asymptotes of 4x^2-24x-25y^2+250y-489=0

asymptotes

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0 :

Up-down Hyperbola with

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

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

25 y^{2} - 81 x^{2} = 2025

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

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

y^{2} - x^{2} = 4

What is the asymptotes of 4x^2-24x-25y^2+250y-489=0 ?
The asymptotes of 4x^2-24x-25y^2+250y-489=0 is y= 2/5 (x-3)+5,\quad y=-2/5 (x-3)+5