What is 3x^2-9y^2-18x+18y-54=0 ?

The solution to 3x^2-9y^2-18x+18y-54=0 is Hyperbola with (h,k)=(3,1),a=2sqrt(6),b=2sqrt(2)

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3x^2-9y^2-18x+18y-54=0

3 x^{2} - 9 y^{2} - 18 x + 18 y - 54 = 0

(h, k) = (3, 1), a = 26, b = 22

Solution steps

3 x^{2} - 9 y^{2} - 18 x + 18 y - 54 = 0

Rewrite

3 x^{2} - 9 y^{2} - 18 x + 18 y - 54 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{( 2 6 ) ^{2}} - \frac{( y - 1 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = 26, b = 22

p^{2} = 32 + q^{2}

\frac{( x - 3 ) ^{2}}{( 3 ) ^{2}} - \frac{( y + 5 ) ^{2}}{( 6 ) ^{2}} = 1

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

5 x^{2} - 4 y^{2} - 20 = 0

4 x^{2} - 25 y^{2} + 50 y - 125 = 0

What is 3x^2-9y^2-18x+18y-54=0 ?
The solution to 3x^2-9y^2-18x+18y-54=0 is Hyperbola with (h,k)=(3,1),a=2sqrt(6),b=2sqrt(2)