What is the foci 25x^2+4y^2+100x=0 ?

The foci 25x^2+4y^2+100x=0 is (-2,sqrt(21)),(-2,-sqrt(21))

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foci 25x^2+4y^2+100x=0

foci

25 x^{2} + 4 y^{2} + 100 x = 0

(- 2, 21), (- 2, - 21)

Solution steps

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

Calculate ellipse properties

25 x^{2} + 4 y^{2} + 100 x = 0 :

Ellipse with center

(h, k) = (- 2, 0), b = 5, a = 2

(- 2, 0 + c), (- 2, 0 - c)

Compute

c :

c = 5^{2} - 2^{2} : 21

(- 2, 0 + 21), (- 2, 0 - 21)

Refine

(- 2, 21), (- 2, - 21)

\frac{x ^{2}}{9 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1

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

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

\frac{( y + 3 ) ^{2}}{169} + \frac{( x + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1

What is the foci 25x^2+4y^2+100x=0 ?
The foci 25x^2+4y^2+100x=0 is (-2,sqrt(21)),(-2,-sqrt(21))