What is (y-3)^2-9(x-3)^2=9 ?

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

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(y-3)^2-9(x-3)^2=9

(y - 3)^{2} - 9 (x - 3)^{2} = 9

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

Solution steps

(y - 3)^{2} - 9 (x - 3)^{2} = 9

Rewrite

(y - 3)^{2} - 9 (x - 3)^{2} = 9

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - y^{2} + 6 x = 19

x^{2} - y^{2} + 6 x = 11

\frac{( x - 0 ) ^{2}}{4} - \frac{( y - ( - 1 ) ) ^{2}}{16} = 1

\frac{y ^{2}}{2} + 3 y = \frac{x ^{2}}{2}

20 (x - y) = 5 x^{2} - 4 y^{2}

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