Question

Two lines PQ and PR are drawn from a point on the circle x² + y² = 25 to the ellipse x²/4² + y²/b² = 1  where b < 4. If the parallelogram PQSR is completed and S lies on the circumcircle of ΔPQR, then the eccentricity of ellipse is

(a)  √7/3

(b)  √5/4

(c) √5/3

(b) √7/4

Answer 1

Correct option (b) √7/4

Explanation :

 Since the points P, Q, S and R concyclic and PQSR is a parallelogram, the angles of the parallelogram are equal to 90°. Hence, P lies on the director circle of

x²/4 + y²/b² = 1

 which is given by x² + y² = 25. Hence, b = 3. Therefor