What is 9x^2-y^2-36x-6y+18=0 ?

The solution to 9x^2-y^2-36x-6y+18=0 is Hyperbola with (h,k)=(2,-3),a=1,b=3

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9x^2-y^2-36x-6y+18=0

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

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

Solution steps

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

Rewrite

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

9 y^{2} - 16 x^{2} = 144

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

16 x^{2} + 25 y^{2} = 400

\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1

4 \leq - x^{2} - y

What is 9x^2-y^2-36x-6y+18=0 ?
The solution to 9x^2-y^2-36x-6y+18=0 is Hyperbola with (h,k)=(2,-3),a=1,b=3