What is -x^2+9y^2+4x+54y+68=0 ?

The solution to -x^2+9y^2+4x+54y+68=0 is Hyperbola with (h,k)=(2,-3),a=1,b=3

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-x^2+9y^2+4x+54y+68=0

- x^{2} + 9 y^{2} + 4 x + 54 y + 68 = 0

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

Solution steps

- x^{2} + 9 y^{2} + 4 x + 54 y + 68 = 0

Rewrite

- x^{2} + 9 y^{2} + 4 x + 54 y + 68 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x = - \frac{1}{8} y^{2}

4 x^{2} - y^{2} = 16

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

x^{2} = - 4 y

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

What is -x^2+9y^2+4x+54y+68=0 ?
The solution to -x^2+9y^2+4x+54y+68=0 is Hyperbola with (h,k)=(2,-3),a=1,b=3