elipses 3

Question

Find the center, vertices, and foci of the ellipse with equation  = 1

Answer 1

The equation of ellipse is x² /400+y² / 250= 1.         (a>b)

Compare the equation (x - 0)²/400 + (y - 0)²/200 = 1 with (x - h)²/b² + (y - k)²/a² = 1.

b² = 250, a² = 400, h = 0 and k = 0.

b = √250 = 5√10 and a = √400 = 20 .

To find the value of c, substitute the value of a² = 400 and b² = 250 in c² = a² - b².

c² = 400 - 250

c² =150

c = ± √150 =± 5√6 .

Center = (h, k ) = (0, 0).

Foci = (h, k ± c) = (0, 0 ± 5√6) = (0, 5√6) and (0, -5√6).

vertices are (h, k ± a) = (0, 0 ± 20) = (0, 20) and (0, -20).