What is x^2-2y^2-4x-4y-400=0 ?

The solution to x^2-2y^2-4x-4y-400=0 is Hyperbola with (h,k)=(2,-1),a=sqrt(402),b=sqrt(201)

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x^2-2y^2-4x-4y-400=0

x^{2} - 2 y^{2} - 4 x - 4 y - 400 = 0

(h, k) = (2, - 1), a = 402, b = 201

Solution steps

x^{2} - 2 y^{2} - 4 x - 4 y - 400 = 0

Rewrite

x^{2} - 2 y^{2} - 4 x - 4 y - 400 = 0

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{( 402 ) ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{( 201 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 1), a = 402, b = 201

9 x^{2} - 16 y^{2} - 36 x - 32 y - 124 = 0

5 x^{2} - 4 y^{2} + 80 = 0

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

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

\frac{x ^{2}}{16 + ( y - 4 ) ^{2}} = 1

What is x^2-2y^2-4x-4y-400=0 ?
The solution to x^2-2y^2-4x-4y-400=0 is Hyperbola with (h,k)=(2,-1),a=sqrt(402),b=sqrt(201)