What is the asymptotes of 5(y+3)^2-4(x-1)^2=20 ?

The asymptotes of 5(y+3)^2-4(x-1)^2=20 is y= 2/(sqrt(5))(x-1)-3,\quad y=-2/(sqrt(5))(x-1)-3

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asymptotes of 5(y+3)^2-4(x-1)^2=20

asymptotes

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

y = \frac{2}{5} (x - 1) - 3, y = - \frac{2}{5} (x - 1) - 3

Solution steps

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

Calculate Hyperbola properties

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20 :

Up-down Hyperbola with

(h, k) = (1, - 3), a = 2, b = 5

y = \frac{2}{5} (x - 1) + (- 3), y = - \frac{2}{5} (x - 1) + (- 3)

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

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

36 x^{2} - 25 y^{2} = 900

x^{2} - y^{2} + 7 x + 8 y = 5

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

What is the asymptotes of 5(y+3)^2-4(x-1)^2=20 ?
The asymptotes of 5(y+3)^2-4(x-1)^2=20 is y= 2/(sqrt(5))(x-1)-3,\quad y=-2/(sqrt(5))(x-1)-3