What is the asymptotes of 4x^2-25y^2+16x+50y-109=0 ?

The asymptotes of 4x^2-25y^2+16x+50y-109=0 is y= 2/5 (x+2)+1,\quad y=-2/5 (x+2)+1

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asymptotes of 4x^2-25y^2+16x+50y-109=0

asymptotes

4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0 :

Right-left Hyperbola with

(h, k) = (- 2, 1), a = 5, b = 2

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

Refine

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

(\frac{x}{2})^{2} - (\frac{y}{3})^{2} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1

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

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

What is the asymptotes of 4x^2-25y^2+16x+50y-109=0 ?
The asymptotes of 4x^2-25y^2+16x+50y-109=0 is y= 2/5 (x+2)+1,\quad y=-2/5 (x+2)+1