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

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

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

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

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

Solution steps

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

Rewrite

4 x^{2} - 12 y^{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}

y = \frac{273 x}{340 y} x + \frac{240000}{340}

\frac{y ^{2}}{4} - \frac{x ^{2}}{12} = 1

4 (x + 5)^{2} - 4 y^{2} = 20

\frac{( x - 27 ) ^{2}}{6} - \frac{( y - 4 ) ^{2}}{10} = 1

x^{2} - y^{2} - 2 x - 4 y - 4 = 0

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