What is x^2-y^2-4x+4y+9=0 ?

The solution to x^2-y^2-4x+4y+9=0 is Hyperbola with (h,k)=(2,2),a=3,b=3

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x^2-y^2-4x+4y+9=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = x^{2} - 4 x

\frac{( x + 1 ) ^{2}}{25} - \frac{( y - 4 ) ^{2}}{144} = 1

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

x^{2} - 4 y^{2} - 4 = 0

16 x^{2} - 96 x - y^{2} - 2 y + 139 = 0

What is x^2-y^2-4x+4y+9=0 ?
The solution to x^2-y^2-4x+4y+9=0 is Hyperbola with (h,k)=(2,2),a=3,b=3