What is 2x^2-2y^2-20x+8y+34=0 ?

The solution to 2x^2-2y^2-20x+8y+34=0 is Hyperbola with (h,k)=(5,2),a=2,b=2

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2x^2-2y^2-20x+8y+34=0

2 x^{2} - 2 y^{2} - 20 x + 8 y + 34 = 0

(h, k) = (5, 2), a = 2, b = 2

Solution steps

2 x^{2} - 2 y^{2} - 20 x + 8 y + 34 = 0

Rewrite

2 x^{2} - 2 y^{2} - 20 x + 8 y + 34 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, 2), a = 2, b = 2

y^{2} - 16 x^{2} + 64 x - 200 = 0

4 x^{2} - 5 y^{2} - 24 y - 16 = 0

- 3 x^{2} + y^{2} - 12 = 0

y^{2} = 4 x^{2} + 3 x + 2

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

What is 2x^2-2y^2-20x+8y+34=0 ?
The solution to 2x^2-2y^2-20x+8y+34=0 is Hyperbola with (h,k)=(5,2),a=2,b=2