What is 4x^2+24x-9y^2+54y-81=0 ?

The solution to 4x^2+24x-9y^2+54y-81=0 is Hyperbola with (h,k)=(-3,3),a=3,b=2

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4x^2+24x-9y^2+54y-81=0

4 x^{2} + 24 x - 9 y^{2} + 54 y - 81 = 0

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

Solution steps

4 x^{2} + 24 x - 9 y^{2} + 54 y - 81 = 0

Rewrite

4 x^{2} + 24 x - 9 y^{2} + 54 y - 81 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

y^{2} - 4 x^{2} - 16 x - 2 y - 19 = 0

9 x^{2} - 16 y^{2} + 144 = 0

36 (y + 4)^{2} - 16 (x - 3)^{2} = 576

(x - 2)^{2} - (y + 3)^{2} = 12

What is 4x^2+24x-9y^2+54y-81=0 ?
The solution to 4x^2+24x-9y^2+54y-81=0 is Hyperbola with (h,k)=(-3,3),a=3,b=2