What is the foci 4x^2+25y^2-50y=75 ?

The foci 4x^2+25y^2-50y=75 is (sqrt(21),1),(-sqrt(21),1)

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foci 4x^2+25y^2-50y=75

foci

4 x^{2} + 25 y^{2} - 50 y = 75

(21, 1), (- 21, 1)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 25 y^{2} - 50 y = 75 :

Ellipse with center

(h, k) = (0, 1), a = 5, b = 2

(0 + c, 1), (0 - c, 1)

Compute

c :

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

(0 + 21, 1), (0 - 21, 1)

Refine

(21, 1), (- 21, 1)

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

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

\frac{( x - 5 ) ^{2}}{3} + \frac{( y - 7 ) ^{2}}{6} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{50} = 1

\frac{x ^{2}}{49} + \frac{y ^{2}}{81} = 1

What is the foci 4x^2+25y^2-50y=75 ?
The foci 4x^2+25y^2-50y=75 is (sqrt(21),1),(-sqrt(21),1)