What is 6x^2-9y^2+96x+36y+252=0 ?

The solution to 6x^2-9y^2+96x+36y+252=0 is Hyperbola with (h,k)=(-8,2),a=4,b=(4sqrt(2))/(sqrt(3))

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6x^2-9y^2+96x+36y+252=0

6 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

(h, k) = (- 8, 2), a = 4, b = \frac{4 2}{3}

Solution steps

6 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

Rewrite

6 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 8 ) ) ^{2}}{4 ^{2}} - \frac{( y - 2 ) ^{2}}{( \frac{4 2}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 8, 2), a = 4, b = \frac{4 2}{3}

x^{2} = y^{2} + 3

\frac{( y + 4 ) ^{2}}{16} - \frac{( x - 3 ) ^{2}}{25} = 1

36 x^{2} - 64 y^{2} = 2304

16 x^{2} - 25 y^{2} - 256 x - 150 y + 399 = 0

12 y^{2} - 4 x^{2} + 16 x + 72 y + 44 = 0

What is 6x^2-9y^2+96x+36y+252=0 ?
The solution to 6x^2-9y^2+96x+36y+252=0 is Hyperbola with (h,k)=(-8,2),a=4,b=(4sqrt(2))/(sqrt(3))