Question

The condition that the chord x cos α + y cosα = p subtends a right angle at the centre of the circle x² + y² = a² is

(A)  a² =  2p²

(B)  p² = 2a²

(C)  a = 2p 

(D)  p = 2a

Answer 1

Correct option (a) a² = 2p²

Explanation :

Suppose the chord x cosα + y cosα = p meets the circle at points A and B (see Fig). Therefore, the combined equation of the pair of lines OA and OB is

Since ∠AOB = 90° , in the above equation, the sum of the coefficient of x² and the coefficient of y² is 0. That is,