What is 9(y-2)^2-4x^2=36 ?

The solution to 9(y-2)^2-4x^2=36 is Hyperbola with (h,k)=(0,2),a=2,b=3

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9(y-2)^2-4x^2=36

9 (y - 2)^{2} - 4 x^{2} = 36

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

Solution steps

9 (y - 2)^{2} - 4 x^{2} = 36

Rewrite

9 (y - 2)^{2} - 4 x^{2} = 36

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} + 9 y^{2} = 9

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1

x = - \frac{1}{8} y^{2}

y^{2} = - 32 x

What is 9(y-2)^2-4x^2=36 ?
The solution to 9(y-2)^2-4x^2=36 is Hyperbola with (h,k)=(0,2),a=2,b=3