What is the foci (x^2)/(16)+((y-1)^2)/(36)=1 ?

The foci (x^2)/(16)+((y-1)^2)/(36)=1 is (0,1+2sqrt(5)),(0,1-2sqrt(5))

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foci (x^2)/(16)+((y-1)^2)/(36)=1

foci

\frac{x ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

(0, 1 + 25), (0, 1 - 25)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1 :

Ellipse with center

(h, k) = (0, 1), b = 6, a = 4

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

Compute

c :

c = 6^{2} - 4^{2} : 25

(0, 1 + 25), (0, 1 - 25)

\frac{( x + 2 ) ^{2}}{10} + \frac{( y - 5 ) ^{2}}{2} = 1

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{81} = 1

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

25 x^{2} + 9 y^{2} - 225 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{25} = 1

What is the foci (x^2)/(16)+((y-1)^2)/(36)=1 ?
The foci (x^2)/(16)+((y-1)^2)/(36)=1 is (0,1+2sqrt(5)),(0,1-2sqrt(5))