What is 4x^2-9y^2+8x+36y-68=0 ?

The solution to 4x^2-9y^2+8x+36y-68=0 is Hyperbola with (h,k)=(-1,2),a=3,b=2

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4x^2-9y^2+8x+36y-68=0

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

(h, k) = (- 1, 2), a = 3, b = 2

Solution steps

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

Rewrite

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 2), a = 3, b = 2

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

3 x^{2} - 12 x - \frac{y ^{2}}{4} - \frac{y}{2} + \frac{43}{4} = 0

- x^{2} + 3 y^{2} - 4 x + 6 y = 28

\frac{y ^{2}}{1} - \frac{x ^{2}}{15} = 1

\frac{( x - 2 ) ^{2}}{36} - \frac{( y + 1 ) ^{2}}{64} = 1

What is 4x^2-9y^2+8x+36y-68=0 ?
The solution to 4x^2-9y^2+8x+36y-68=0 is Hyperbola with (h,k)=(-1,2),a=3,b=2