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

The foci 2x^2-2y^2-20x+16y-16=0 is (5+sqrt(34),4),(5-sqrt(34),4)

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

foci

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

(5 + 34, 4), (5 - 34, 4)

Solution steps

(h + c, k), (h - c, k)

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

(5 + c, 4), (5 - c, 4)

Compute

c :

c = 17^{2} + 17^{2} : 34

(5 + 34, 4), (5 - 34, 4)

\frac{y ^{2}}{25} - \frac{x ^{2}}{36} = 1

\frac{( x - 1 ) ^{2}}{12} - \frac{( y - 2 ) ^{2}}{8} = 1

- x^{2} + 25 \cdot y^{2} = 25

4 x^{2} - y^{2} + 12 x + 5 = 0

\frac{( x - 13 ) ^{2}}{144} - \frac{y ^{2}}{25} = 1

What is the foci 2x^2-2y^2-20x+16y-16=0 ?
The foci 2x^2-2y^2-20x+16y-16=0 is (5+sqrt(34),4),(5-sqrt(34),4)