What is -x^2+9y^2-36y+27=0 ?

The solution to -x^2+9y^2-36y+27=0 is Hyperbola with (h,k)=(0,2),a=1,b=3

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-x^2+9y^2-36y+27=0

- x^{2} + 9 y^{2} - 36 y + 27 = 0

(h, k) = (0, 2), a = 1, b = 3

Solution steps

- x^{2} + 9 y^{2} - 36 y + 27 = 0

Rewrite

- x^{2} + 9 y^{2} - 36 y + 27 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 2), a = 1, b = 3

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

\frac{( x - 1 ) ^{2}}{49} - \frac{( y + 3 ) ^{2}}{9} = 1

(y - 3) (y + 1) - (2 x + 1) (x - 3) = 0

x^{2} - 3 y^{2} + 6 y + 6 = 0

9 y^{2} - 16 x^{2} + 18 y + 64 x - 199 = 0

What is -x^2+9y^2-36y+27=0 ?
The solution to -x^2+9y^2-36y+27=0 is Hyperbola with (h,k)=(0,2),a=1,b=3