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

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

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asymptotes of x^2-4(y-3)^2=4

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 3), a = 2, b = 1

y = \frac{1}{2} (x - 0) + 3, y = - \frac{1}{2} (x - 0) + 3

Refine

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

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

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0

x^{2} - 16 y^{2} = 16

- \frac{y ^{2}}{1} + \frac{x ^{2}}{49} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

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