Question

Point O is the centre of an ellipse with major axis (bar)AB and minor axis CD. Point F is one of the foci. If OF = 6 and the diameter of the inscribed circle of ΔOCF is 2, then (AB)(CD) =

 (A)  35

(B)  45 

(C)  55 

(D)  65

Answer 1

Correct option (D)  65

Explanation :

See Fig. Let OC = b, OF = 6 and CF = a. Sinc 

1 =  Inradius of  ΔOCF

= (1/2)(b)(6)/(1/2)(b + 6 + a)

b + 6 + a = 6b

5b = 6 + a  ...(1)

Also

36 = a²e² = a² - b² ....(2)

From Eqs. (1) and (2), we have