Find the vertices and foci of ellipse with equation xsquared/4+ysquared/16=1?

Answer 1

The ellipse is:

x²/4 + y²/16 = 1

The center of the ellipse (h,k) = (0, 0).

a² = 16
a = 4

b² = 4
b = 2

c² = a² - b² = 16 - 4 = 12
c =√12 = 2√3

Since the ellipse is vertical the vertices are:

(h, k + a) and (h, k - a) or (0, 4) and (0, -4).

The foci are:

(h, k + c) and (h, k - c) or (0, 2√3) and (0, -2√3).