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(2),4),(5-sqrt(2),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 + 2, 4), (5 - 2, 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 = 1, b = 1

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

Compute

c :

c = 1^{2} + 1^{2} : 2

(5 + 2, 4), (5 - 2, 4)

25 y^{2} - 16 x^{2} - 400 = 0

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{49} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{144} = 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(2),4),(5-sqrt(2),4)