Question

Let L₁ be a straight line passing through the origin and L₂ be the 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 equations can represent by L₁ .

(A)  x + y = 0

(B)  x - y = 0

(C)  2x + 7y = 0

(D)  x - 7y = 0

Answer 1

Correct option (B) x - y = 0 

Explanation :

Centre of the circle is (1/2, 3/2) and the radius of the circle is √5 /2 . Let P be the length of the perpendicular from the centre (1/2, 3/2) onto the line L₂. Therefore

Let y = mx be the equation of L₁ . Hence, we have

4 = (m + 3)²/2(l + m²)

so that m = 1 or –1/7. Here m = 1 implies that the equations of L₁ is y = x or x – y = 0.