What is 9x^{(2)}-36x-16y^{(2)}-32y=124 ?

The solution to 9x^{(2)}-36x-16y^{(2)}-32y=124 is Hyperbola with (h,k)=(2,-1),a=4,b=3

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9x^{(2)}-36x-16y^{(2)}-32y=124

9 x^{(2)} - 36 x - 16 y^{(2)} - 32 y = 124

(h, k) = (2, - 1), a = 4, b = 3

Solution steps

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

Rewrite

9 x^{2} - 36 x - 16 y^{2} - 32 y = 124

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 1), a = 4, b = 3

y = (x^{2} - y^{2})

4 x^{2} - 24 x - 36 y^{2} - 360 y + 864 = 0

x^{2} - 6 x - 6 = y^{2} + 6 y + 6

y^{2} = 2 x^{2} + 8

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

What is 9x^{(2)}-36x-16y^{(2)}-32y=124 ?
The solution to 9x^{(2)}-36x-16y^{(2)}-32y=124 is Hyperbola with (h,k)=(2,-1),a=4,b=3