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

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

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

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

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

Solution steps

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

Rewrite

9 x^{2} - 36 x - y^{2} - 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

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

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

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

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

\frac{x ^{2}}{1 8 ^{2}} - \frac{y ^{2}}{3 5 ^{2}} = 1

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