What is 18x^2-9y^2-96x-36y-36=0 ?

The solution to 18x^2-9y^2-96x-36y-36=0 is Hyperbola with (h,k)=(8/3 ,-2),a= 8/3 ,b=(8sqrt(2))/3

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18x^2-9y^2-96x-36y-36=0

18 x^{2} - 9 y^{2} - 96 x - 36 y - 36 = 0

(h, k) = (\frac{8}{3}, - 2), a = \frac{8}{3}, b = \frac{8 2}{3}

Solution steps

18 x^{2} - 9 y^{2} - 96 x - 36 y - 36 = 0

Rewrite

18 x^{2} - 9 y^{2} - 96 x - 36 y - 36 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{8}{3} ) ^{2}}{( \frac{8}{3} ) ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{( \frac{8 2}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{8}{3}, - 2), a = \frac{8}{3}, b = \frac{8 2}{3}

\frac{x ^{2}}{14} - \frac{y ^{2}}{20} = 1

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

x^{2} = 280 0^{2} + y^{2} - 2 (2800) (y) cos (2 0^{\circ})

x^{2} - (y - 3960)^{2} = 396 0^{2}

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2304 = 0

What is 18x^2-9y^2-96x-36y-36=0 ?
The solution to 18x^2-9y^2-96x-36y-36=0 is Hyperbola with (h,k)=(8/3 ,-2),a= 8/3 ,b=(8sqrt(2))/3