Question

Let L₁ be a straight line passing through the origin and L₂ be the straight line x + y = 1. If the intercepts made by the circle x² + y² - x + 3y = 0 on L₁ and L₂ are equal, then which of the following equation can represent L₁?

(a) x + y = 0

(b) x - y = 0

(c) x + 7y = 0

(d) x - 7y = 0

Answer 1

Correct option: (b) x - y = 0, (c) x + 7y = 0

Explanation:

Let equation of line L₁ be y = mx. Intercepts made by L₁ and L₂ on the circle will be equal ie, L₁ and L₂ are at the same distance from the centre of the circle.

Centre of the given circle is (1/ 2, - 3/2). Therefore,

Thus, two chords are x + 7 y = 0 and y - x = 0

Therefore, (b) and (c) are correct answers.