What is x^{(2)}-y^{(2)}-2x+4y-6=0 ?

The solution to x^{(2)}-y^{(2)}-2x+4y-6=0 is Hyperbola with (h,k)=(1,2),a=sqrt(3),b=sqrt(3)

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x^{(2)}-y^{(2)}-2x+4y-6=0

x^{(2)} - y^{(2)} - 2 x + 4 y - 6 = 0

(h, k) = (1, 2), a = 3, b = 3

Solution steps

x^{2} - y^{2} - 2 x + 4 y - 6 = 0

Rewrite

x^{2} - y^{2} - 2 x + 4 y - 6 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 3, b = 3

\frac{x ^{2}}{16} - \frac{y ^{2}}{49} = 1

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

4 x^{2} - 9 y^{2} - 11 = 0

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

\frac{3}{2} (v - \frac{3}{2})^{2} - \frac{1}{2} (u + \frac{3}{2})^{2} = 6

What is x^{(2)}-y^{(2)}-2x+4y-6=0 ?
The solution to x^{(2)}-y^{(2)}-2x+4y-6=0 is Hyperbola with (h,k)=(1,2),a=sqrt(3),b=sqrt(3)