What is x^2+11=y^2+4x-2y ?

The solution to x^2+11=y^2+4x-2y is Hyperbola with (h,k)=(2,1),a=2sqrt(2),b=2sqrt(2)

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x^2+11=y^2+4x-2y

x^{2} + 11 = y^{2} + 4 x - 2 y

(h, k) = (2, 1), a = 22, b = 22

Solution steps

x^{2} + 11 = y^{2} + 4 x - 2 y

Rewrite

x^{2} + 11 = y^{2} + 4 x - 2 y

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 22, b = 22

\frac{( x - 1 ) ^{2}}{4} - \frac{y ^{2}}{5} = 1

8^{2} + (x - 2)^{2} = y^{2}

- \frac{9}{5} + 2 x + x^{2} - \frac{6 y}{5} - \frac{y ^{2}}{5} = 0

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

240 0^{2} x^{2} = 46 0^{2} (x^{2} + z^{2} + 36)

What is x^2+11=y^2+4x-2y ?
The solution to x^2+11=y^2+4x-2y is Hyperbola with (h,k)=(2,1),a=2sqrt(2),b=2sqrt(2)