What is the foci ((y-1)^2)/4+((x^2))/(25)=1 ?

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

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foci ((y-1)^2)/4+((x^2))/(25)=1

foci

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

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

Solution steps

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

Calculate ellipse properties

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

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} - 4 x - 8 y - 92 = 0

x^{2} + 9 y^{2} = 36

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

\frac{( x - 6 ) ^{2}}{49} + \frac{( y - 6 ) ^{2}}{36} = 1

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

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