What is 12y^2-4x^2+24x-24y-51=0 ?

The solution to 12y^2-4x^2+24x-24y-51=0 is Hyperbola with (h,k)=(3,1),a= 3/2 ,b=(3sqrt(3))/2

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12y^2-4x^2+24x-24y-51=0

12 y^{2} - 4 x^{2} + 24 x - 24 y - 51 = 0

(h, k) = (3, 1), a = \frac{3}{2}, b = \frac{3 3}{2}

Solution steps

12 y^{2} - 4 x^{2} + 24 x - 24 y - 51 = 0

Rewrite

12 y^{2} - 4 x^{2} + 24 x - 24 y - 51 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = \frac{3}{2}, b = \frac{3 3}{2}

4 y^{2} - 9 x^{2} - 36 x + 8 y = 0

16.99 y^{2} = 32 + 15.93 x^{2}

25 x^{2} - 200 x - 9 y^{2} + 36 y = 139

\frac{( y - 5 ) ^{2}}{16} - \frac{( x + 4 ) ^{2}}{4} = 1

- 4 x^{2} + 56 x + y^{2} - 188 = 0

What is 12y^2-4x^2+24x-24y-51=0 ?
The solution to 12y^2-4x^2+24x-24y-51=0 is Hyperbola with (h,k)=(3,1),a= 3/2 ,b=(3sqrt(3))/2