What is (x^2)/9+(2x)/3-9y^2-54y-81=0 ?

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

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(x^2)/9+(2x)/3-9y^2-54y-81=0

\frac{x ^{2}}{9} + \frac{2 x}{3} - 9 y^{2} - 54 y - 81 = 0

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

Solution steps

\frac{x ^{2}}{9} + \frac{2 x}{3} - 9 y^{2} - 54 y - 81 = 0

Rewrite

\frac{x ^{2}}{9} + \frac{2 x}{3} - 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}}{( \frac{1}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

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

\frac{1}{36} x^{2} - \frac{1}{4} y^{2} = 1

\frac{x ^{2}}{32} - \frac{y ^{2}}{25} = 1

yy = x^{2} - 9

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

x^{2} - 9 y^{2} = 36

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