Question

Consider an ellipse with foci at (5, 15) and (21, 15). If the x-axis touches the ellipse, then the length of the major axis is

(a)  17

(b)  34

(c)  13

(d)  √416

Answer 1

Correct option  (B)  34

Explanation :

The major axis is y = 15. The distance between the foci is

2ae = 16 ⇒ ae = 8

Since x-axis is touching the ellipse, we have b = 15 so that

15² = b² = a²(1 - e²) = a² - 64

⇒ a = 17 and e = 8/17

Therefore, the length of the major axis is 2a = 2 x 17 = 34