What is the foci 4x^2+25y^2-24x+250y+561=0 ?

The foci 4x^2+25y^2-24x+250y+561=0 is (3+sqrt(21),-5),(3-sqrt(21),-5)

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foci 4x^2+25y^2-24x+250y+561=0

foci

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

(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 = 0 :

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)

14 x^{2} - 70 = - 5 y^{2}

- \frac{( y - 1 ) ^{2}}{144} - \frac{( x + 2 ) ^{2}}{9} = 1

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

x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

y^{2} = 1 - 4 x^{2}

What is the foci 4x^2+25y^2-24x+250y+561=0 ?
The foci 4x^2+25y^2-24x+250y+561=0 is (3+sqrt(21),-5),(3-sqrt(21),-5)