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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

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

6 x^{2} - 3 y^{2} - 6 x - 3 y + 78 = 0

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

16 x^{2} - 9 y^{2} - 96 x - 18 y - 9 = 0

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