What is x^2-6x-9y^2-54y-81=0 ?

The solution to x^2-6x-9y^2-54y-81=0 is Hyperbola with (h,k)=(3,-3),a=3,b=1

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x^2-6x-9y^2-54y-81=0

x^{2} - 6 x - 9 y^{2} - 54 y - 81 = 0

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

Solution steps

x^{2} - 6 x - 9 y^{2} - 54 y - 81 = 0

Rewrite

x^{2} - 6 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}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

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

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

9 x^{2} - 4 y^{2} + 90 x + 189 = 0

3 x^{2} - y^{2} + 7 x - y + 18 = 0

- x^{2} + 4 x + 3 y^{2} - 18 y + 8 = 0

7 x^{2} - 9 y^{2} = 63

What is x^2-6x-9y^2-54y-81=0 ?
The solution to x^2-6x-9y^2-54y-81=0 is Hyperbola with (h,k)=(3,-3),a=3,b=1