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

The solution to 4x^2-9y^2+4x+36y-36=0 is Hyperbola with (h,k)=(-1/2 ,2),a= 1/2 ,b= 1/3

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

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

(h, k) = (- \frac{1}{2}, 2), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{2}, 2), a = \frac{1}{2}, b = \frac{1}{3}

9 x^{2} - 16 y^{2} - 36 x + 96 y - 252 = 0

\frac{x ^{2} - 8 x + 16}{16} - \frac{y ^{2} + 4 y - 4}{9} = 0

50 x^{2} - 25 y^{2} + 144 x - 68 y - 75 = 0

4 x^{2} - y^{2} - 20 x - 10 y + 25 = 0

\frac{x ^{2}}{0.0008} - \frac{y ^{2}}{0.999} = 1

What is 4x^2-9y^2+4x+36y-36=0 ?
The solution to 4x^2-9y^2+4x+36y-36=0 is Hyperbola with (h,k)=(-1/2 ,2),a= 1/2 ,b= 1/3