What is x^2-y^2-2x-4y-7=0 ?

The solution to x^2-y^2-2x-4y-7=0 is Hyperbola with (h,k)=(1,-2),a=2,b=2

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x^2-y^2-2x-4y-7=0

x^{2} - y^{2} - 2 x - 4 y - 7 = 0

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

Solution steps

x^{2} - y^{2} - 2 x - 4 y - 7 = 0

Rewrite

x^{2} - y^{2} - 2 x - 4 y - 7 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

y \frac{1}{3} y - x^{2} + 2 x = - 5

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

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

\frac{( x - 3 ) ^{2}}{6} - \frac{( y - 1 ) ^{2}}{12} = 1

What is x^2-y^2-2x-4y-7=0 ?
The solution to x^2-y^2-2x-4y-7=0 is Hyperbola with (h,k)=(1,-2),a=2,b=2