What is x^2-y^2+4x-2y-5=0 ?

The solution to x^2-y^2+4x-2y-5=0 is Hyperbola with (h,k)=(-2,-1),a=2sqrt(2),b=2sqrt(2)

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x^2-y^2+4x-2y-5=0

x^{2} - y^{2} + 4 x - 2 y - 5 = 0

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

Solution steps

x^{2} - y^{2} + 4 x - 2 y - 5 = 0

Rewrite

x^{2} - y^{2} + 4 x - 2 y - 5 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{1} - \frac{y ^{2}}{15} = 1

x^{2} - 4 y^{2} + 6 x + 24 y - 31 = 0

x^{2} - 4 y^{2} - 6 x + 16 y + 21 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{5} = 1

yy = (x + 7)^{2} + 3

What is x^2-y^2+4x-2y-5=0 ?
The solution to x^2-y^2+4x-2y-5=0 is Hyperbola with (h,k)=(-2,-1),a=2sqrt(2),b=2sqrt(2)