Find the foci of the ellipse 4x2 25y2 100y 0 Solution4x2

Find the foci of the ellipse. 4x^2 + 25y^2 - 100y = 0

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

Dividing by 100 throughout,

x^2/25 + y^2/4 - y = 0

Adding 1 both sides

x^2/25 + y^2/4 - y + 4/4 = 1

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

Comparing it with standard equation of ellipse,

(xh)^2/a^2+(yk^)2/b^2 = 1

we see h = 0, k = 2, a = 5, b = 2 Hence c = sqrt(25 - 4) = sqrt(21)

Hence the foci of ellipse is (h+c, k) and (h-c, k) i.e (sqrt(21), 2) and (-sqrt(21), 2)