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

Therefore Hyperbola properties are:

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

25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

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

9 x^{2} - 4 y^{2} + 54 x + 8 y + 78 = 0

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 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=3,b=2