What is 9x^2-y^2-36x-6y+36=0 ?

The solution to 9x^2-y^2-36x-6y+36=0 is Hyperbola with (h,k)=(2,-3),a=3,b=1

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9x^2-y^2-36x-6y+36=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} - x^{2} - 2 x - 3 = 0

yy = x^{2} - 2 x

36 x^{2} - 64 y^{2} - 504 x + 768 y - 2844 = 0

4 x^{2} - 5 y^{2} + 8 x - 10 y + 19 = 0

16 y^{2} - 9 x^{2} - 112 y + 36 x + 124 = 0

What is 9x^2-y^2-36x-6y+36=0 ?
The solution to 9x^2-y^2-36x-6y+36=0 is Hyperbola with (h,k)=(2,-3),a=3,b=1