What is 4x^2-9y^2+8x-36y=0 ?

The solution to 4x^2-9y^2+8x-36y=0 is Hyperbola with (h,k)=(-1,-2),a=(4sqrt(2))/3 ,b=2sqrt(2)

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

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

(h, k) = (- 1, - 2), a = \frac{4 2}{3}, b = 22

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( \frac{4 2}{3} ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 2), a = \frac{4 2}{3}, b = 22

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{81} = 1

\frac{( y - 2 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{4} = 1

\frac{( y - 3 ) ^{2}}{49} - \frac{( x + 2 ) ^{2}}{16} = 1

y^{2} \leq x^{2} + y

What is 4x^2-9y^2+8x-36y=0 ?
The solution to 4x^2-9y^2+8x-36y=0 is Hyperbola with (h,k)=(-1,-2),a=(4sqrt(2))/3 ,b=2sqrt(2)