Question

Point is one of the foci of the ellipse x2/25 + y2/16 = 1 With as centre and r as radius, a circle is drawn such that it touches the ellipse and completely **** within the ellipse. Then, the value of the radius r is

(A) 4

(B) 3

(A) √3

(D) 2

Answer 1

Correct option**(D) 2**

Explanation :

The ellipse is

x2/25 + y2/16 = 1 ⇒ a = 5, b = 4

which implies that a = 5 and b = 4. Also

16 = 25(1 - e2) ⇒ e 3/5

Hence, = (3, 0) (see Fig). Also we know that the vertex A = (5, 0). This implies that SA = 2. Since the circle is touching the ellipse and *** completely within the ellipse, it follows that its radius r must be equal to 2.