What is 2x^2-2y^2-20x+16y-16=0 ?

The solution to 2x^2-2y^2-20x+16y-16=0 is Hyperbola with (h,k)=(5,4),a=sqrt(17),b=sqrt(17)

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2x^2-2y^2-20x+16y-16=0

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

(h, k) = (5, 4), a = 17, b = 17

Solution steps

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

Rewrite

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

in the form of a standard hyperbola equation

\frac{( x - 5 ) ^{2}}{( 17 ) ^{2}} - \frac{( y - 4 ) ^{2}}{( 17 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, 4), a = 17, b = 17

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

(x + 5)^{2} - (y - 7)^{2} = 1

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

\frac{x ^{2}}{49} - \frac{y ^{2}}{44} = 1

x^{2} - y^{2} = 640

What is 2x^2-2y^2-20x+16y-16=0 ?
The solution to 2x^2-2y^2-20x+16y-16=0 is Hyperbola with (h,k)=(5,4),a=sqrt(17),b=sqrt(17)