What is 9x^2-4y^2-18x-16y-11=0 ?

The solution to 9x^2-4y^2-18x-16y-11=0 is Hyperbola with (h,k)=(1,-2),a= 2/3 ,b=1

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9x^2-4y^2-18x-16y-11=0

9 x^{2} - 4 y^{2} - 18 x - 16 y - 11 = 0

(h, k) = (1, - 2), a = \frac{2}{3}, b = 1

Solution steps

9 x^{2} - 4 y^{2} - 18 x - 16 y - 11 = 0

Rewrite

9 x^{2} - 4 y^{2} - 18 x - 16 y - 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = \frac{2}{3}, b = 1

x^{2} - y^{2} - 2 x - 6 y - 12 > 0

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

16 x^{2} - y^{2} - 96 x - 6 y + 119 = 0

\frac{x ^{2}}{40} - \frac{y ^{2}}{120} = 1

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

What is 9x^2-4y^2-18x-16y-11=0 ?
The solution to 9x^2-4y^2-18x-16y-11=0 is Hyperbola with (h,k)=(1,-2),a= 2/3 ,b=1