What is 4(y-3)^2-9(x-2)^2=36 ?

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

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4(y-3)^2-9(x-2)^2=36

4 (y - 3)^{2} - 9 (x - 2)^{2} = 36

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

Solution steps

4 (y - 3)^{2} - 9 (x - 2)^{2} = 36

Rewrite

4 (y - 3)^{2} - 9 (x - 2)^{2} = 36

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

36 x^{2} - y^{2} - 216 x + 10 y + 263 = 0

x^{2} - 4 y^{2} + 8 y - 8 = 0

\frac{x ^{2}}{16} - \frac{( y + 4 ) ^{2}}{81} = 1

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

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