What is (x^2)/9+(8x)/9-(y^2)/9+(8y)/9-1/81 =0 ?

The solution to (x^2)/9+(8x)/9-(y^2)/9+(8y)/9-1/81 =0 is Hyperbola with (h,k)=(-4,4),a= 1/3 ,b= 1/3

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(x^2)/9+(8x)/9-(y^2)/9+(8y)/9-1/81 =0

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

(h, k) = (- 4, 4), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

Rewrite

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 4 ) ) ^{2}}{( \frac{1}{3} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, 4), a = \frac{1}{3}, b = \frac{1}{3}

x^{2} - y^{2} + 2 > 0

3 x^{2} - 2 y^{2} = 30

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

y^{2} - 9 x^{2} - 36 x - 45 = 0

x^{2} - y^{2} - 4 x - 12 y + 15 = 0

What is (x^2)/9+(8x)/9-(y^2)/9+(8y)/9-1/81 =0 ?
The solution to (x^2)/9+(8x)/9-(y^2)/9+(8y)/9-1/81 =0 is Hyperbola with (h,k)=(-4,4),a= 1/3 ,b= 1/3