What is 9x^2-16y^2+36x+32y-124=0 ?

The solution to 9x^2-16y^2+36x+32y-124=0 is Hyperbola with (h,k)=(-2,1),a=4,b=3

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9x^2-16y^2+36x+32y-124=0

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

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

Solution steps

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

Rewrite

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

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

4 x^{2} + 4 y^{2} + 36 y + 5 = 0

x^{2} + \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{9} = 1

x = y^{2} - 1

\frac{( x - 3 ) ^{2}}{81} - \frac{( y + 5 ) ^{2}}{144} = 1

What is 9x^2-16y^2+36x+32y-124=0 ?
The solution to 9x^2-16y^2+36x+32y-124=0 is Hyperbola with (h,k)=(-2,1),a=4,b=3