What is the foci 4x^2-40x+2y^2-20y=-142 ?

The foci 4x^2-40x+2y^2-20y=-142 is (5,5+sqrt(2)),(5,5-sqrt(2))

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foci 4x^2-40x+2y^2-20y=-142

foci

4 x^{2} - 40 x + 2 y^{2} - 20 y = - 142

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

Solution steps

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

Calculate ellipse properties

4 x^{2} - 40 x + 2 y^{2} - 20 y = - 142 :

Ellipse with center

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

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

Compute

c :

c = 2^{2} - 2^{2} : 2

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

9 x^{2} + 7 y^{2} = 63

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 1 ) ^{2}}{49} = 1

\frac{( x + 20 ) ^{2}}{16} + \frac{y ^{2}}{89} = 1

\frac{x ^{2}}{\frac{9}{4}} + \frac{y ^{2}}{\frac{25}{4}} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

What is the foci 4x^2-40x+2y^2-20y=-142 ?
The foci 4x^2-40x+2y^2-20y=-142 is (5,5+sqrt(2)),(5,5-sqrt(2))