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

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

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

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

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

Solution steps

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

Rewrite

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

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

y^{2} = x^{2} - 8

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

4 x^{2} - y^{2} + 8 x - 2 y + 7 = 0

x^{2} + 36 y - 32 x - y^{2} = 75

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

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