What is 9x^2-4y^2-54x+8y-113=0 ?

The solution to 9x^2-4y^2-54x+8y-113=0 is Hyperbola with (h,k)=(3,1),a=(sqrt(190))/3 ,b=sqrt(95/2)

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9x^2-4y^2-54x+8y-113=0

9 x^{2} - 4 y^{2} - 54 x + 8 y - 113 = 0

(h, k) = (3, 1), a = \frac{190}{3}, b = \frac{95}{2}

Solution steps

9 x^{2} - 4 y^{2} - 54 x + 8 y - 113 = 0

Rewrite

9 x^{2} - 4 y^{2} - 54 x + 8 y - 113 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{( \frac{190}{3} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( \frac{95}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = \frac{190}{3}, b = \frac{95}{2}

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{9} = 1

5 y^{2} + 30 y + 8 x - 79 - 4 x^{2} = 0

4 x^{2} - y^{2} - 24 x - 4 y + 16 = 0

\frac{( y - 1 ) ^{2}}{49} - \frac{( x - 2 ) ^{2}}{32} = 1

4 x^{2} + 8 x - 3 y^{2} + 16 = 0

What is 9x^2-4y^2-54x+8y-113=0 ?
The solution to 9x^2-4y^2-54x+8y-113=0 is Hyperbola with (h,k)=(3,1),a=(sqrt(190))/3 ,b=sqrt(95/2)