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

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

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

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

(h, k) = (0, 3), a = 1, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} - \frac{( y - 3 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 3), a = 1, b = 3

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

25 x^{2} + 246 x - 25 y^{2} - 13 y = 233

9 x^{2} - 4 y^{2} - 18 x + 16 y - 43 = 0

16 x^{2} - 9 y^{2} - 144 = 0

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

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