What is 12y^2+72y-4x^2+16x+44=0 ?

The solution to 12y^2+72y-4x^2+16x+44=0 is Hyperbola with (h,k)=(2,-3),a=2,b=2sqrt(3)

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

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

(h, k) = (2, - 3), a = 2, b = 23

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 2, b = 23

(x - 1)^{2} - (y - 4)^{2} = 16

y^{2} = x^{2} + 289

- 3 y^{2} + 18 x^{2} = - y - 2

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{4} = 1

What is 12y^2+72y-4x^2+16x+44=0 ?
The solution to 12y^2+72y-4x^2+16x+44=0 is Hyperbola with (h,k)=(2,-3),a=2,b=2sqrt(3)