What is 36x^2-y^2-24x+6y-41=0 ?

The solution to 36x^2-y^2-24x+6y-41=0 is Hyperbola with (h,k)=(1/3 ,3),a=1,b=6

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36x^2-y^2-24x+6y-41=0

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

(h, k) = (\frac{1}{3}, 3), a = 1, b = 6

Solution steps

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

Rewrite

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{3}, 3), a = 1, b = 6

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

\frac{y ^{2}}{56} - \frac{x ^{2}}{56} = 1

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{4} = 1

4 (y - 4)^{2} - (x - 2)^{2} = 36

What is 36x^2-y^2-24x+6y-41=0 ?
The solution to 36x^2-y^2-24x+6y-41=0 is Hyperbola with (h,k)=(1/3 ,3),a=1,b=6