What is -x^2+9y^2-54y+45=0 ?

The solution to -x^2+9y^2-54y+45=0 is Hyperbola with (h,k)=(0,3),a=2,b=6

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-x^2+9y^2-54y+45=0

- x^{2} + 9 y^{2} - 54 y + 45 = 0

(h, k) = (0, 3), a = 2, b = 6

Solution steps

- x^{2} + 9 y^{2} - 54 y + 45 = 0

Rewrite

- x^{2} + 9 y^{2} - 54 y + 45 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{2 ^{2}} - \frac{( x - 0 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 3), a = 2, b = 6

9 x^{2} - 25 y^{2} - 90 x - 100 y - 100 = 0

\frac{( y ^{2} )}{25} - \frac{( x ^{2} )}{9} = 1

4 x^{2} - 25 y^{2} + 48 + 150 - 181 = 0

9 y^{2} + 36 y - 4 x^{2} - 16 x - 16 = 0

\frac{x ^{2}}{56} - \frac{y ^{2}}{20} = 1

What is -x^2+9y^2-54y+45=0 ?
The solution to -x^2+9y^2-54y+45=0 is Hyperbola with (h,k)=(0,3),a=2,b=6