What is the foci 4x^2+25y^2+24x+250y=-561 ?

The foci 4x^2+25y^2+24x+250y=-561 is (-3+sqrt(21),-5),(-3-sqrt(21),-5)

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foci 4x^2+25y^2+24x+250y=-561

foci

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

(- 3 + 21, - 5), (- 3 - 21, - 5)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561 :

Ellipse with center

(h, k) = (- 3, - 5), a = 5, b = 2

(- 3 + c, - 5), (- 3 - c, - 5)

Compute

c :

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

(- 3 + 21, - 5), (- 3 - 21, - 5)

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

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

16 x^{2} - 96 x + 9 y^{2} = 0

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

What is the foci 4x^2+25y^2+24x+250y=-561 ?
The foci 4x^2+25y^2+24x+250y=-561 is (-3+sqrt(21),-5),(-3-sqrt(21),-5)