What is 9x^2-y^2-36x-2y+44=0 ?

The solution to 9x^2-y^2-36x-2y+44=0 is Hyperbola with (h,k)=(2,-1),a=3,b=1

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9x^2-y^2-36x-2y+44=0

9 x^{2} - y^{2} - 36 x - 2 y + 44 = 0

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

Solution steps

9 x^{2} - y^{2} - 36 x - 2 y + 44 = 0

Rewrite

9 x^{2} - y^{2} - 36 x - 2 y + 44 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

t^{2} = 27 + u^{2}

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{9} + \frac{8 x}{9} - \frac{y ^{2}}{9} + \frac{8 y}{9} - \frac{1}{81} = 0

x^{2} - y^{2} + 2 > 0

3 x^{2} - 2 y^{2} = 30

What is 9x^2-y^2-36x-2y+44=0 ?
The solution to 9x^2-y^2-36x-2y+44=0 is Hyperbola with (h,k)=(2,-1),a=3,b=1