Question

If a tangent of slope 2 of the ellipse x²/a² + y²/b² = 1 is normal to the circle x² + y² + 4x + 1 = 0, then the maximum value of ab is equal to

 (A)  2 

(B)  1 

(C)  4 

(D)  3

Answer 1

Correct option  (c)  4

Explanation :

 y = 2x + √4a² + b²  is a tangent to the ellipse. This passes through the centre (−2, 0) of the circle. Hence

Equality holds when 2a = b. Hence, the maximum value of ab is 4.