What is (x^2-4x+4)-(y^2-6y+9)=9 ?

The solution to (x^2-4x+4)-(y^2-6y+9)=9 is Hyperbola with (h,k)=(2,3),a=3,b=3

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(x^2-4x+4)-(y^2-6y+9)=9

(x^{2} - 4 x + 4) - (y^{2} - 6 y + 9) = 9

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

Solution steps

x^{2} - 4 x + 4 - (y^{2} - 6 y + 9) = 9

Rewrite

x^{2} - 4 x + 4 - (y^{2} - 6 y + 9) = 9

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

a^{2} + 150 = b^{2} + 9

3 x^{2} - 5 y^{2} = 7

\frac{( x - 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{5} = 1

6 x^{(2)} - 5 y^{(2)} + 24 x + 20 y - 56 = 0

\frac{x ^{2}}{49} - \frac{( y + 2 ) ^{2}}{79} = 1

What is (x^2-4x+4)-(y^2-6y+9)=9 ?
The solution to (x^2-4x+4)-(y^2-6y+9)=9 is Hyperbola with (h,k)=(2,3),a=3,b=3