What is the asymptotes of 5y^2-16x^2+400=0 ?

The asymptotes of 5y^2-16x^2+400=0 is y=(4x)/(sqrt(5)),\quad y=-(4x)/(sqrt(5))

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asymptotes of 5y^2-16x^2+400=0

asymptotes

5 y^{2} - 16 x^{2} + 400 = 0

y = \frac{4 x}{5}, y = - \frac{4 x}{5}

Solution steps

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

Calculate Hyperbola properties

5 y^{2} - 16 x^{2} + 400 = 0 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 5, b = 45

y = \frac{4 5}{5} (x - 0) + 0, y = - \frac{4 5}{5} (x - 0) + 0

Refine

y = \frac{4 x}{5}, y = - \frac{4 x}{5}

- 25 x^{2} + y^{2} = 25

5 x^{2} - 6 y^{2} - 20 x + 12 y - 16 = 0

\frac{y ^{2}}{1 2 ^{2}} - \frac{x ^{2}}{6 ^{2}} = 1

x^{2} - 4 (y - 3)^{2} = 4

16 y^{2} - 81 x^{2} - 256 y + 486 x = 1001

What is the asymptotes of 5y^2-16x^2+400=0 ?
The asymptotes of 5y^2-16x^2+400=0 is y=(4x)/(sqrt(5)),\quad y=-(4x)/(sqrt(5))