What is 9x^2-4y^2-36x+72=0 ?

The solution to 9x^2-4y^2-36x+72=0 is Hyperbola with (h,k)=(2,0),a=3,b=2

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9x^2-4y^2-36x+72=0

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

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

Solution steps

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

Rewrite

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{z ^{2}}{4} - y^{2} = 1

\frac{( y + 5 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 9

25 y^{2} - x^{2} + 2 x + 150 y + 225 = 0

\frac{( y + 5 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{16} = 1

What is 9x^2-4y^2-36x+72=0 ?
The solution to 9x^2-4y^2-36x+72=0 is Hyperbola with (h,k)=(2,0),a=3,b=2