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 L₁ may be represented by the equations

(A)  x + y = 0

(B)  x - y = 0

(C)  x + 7y = 0

(D)  x - 7y = 0

Answer 1

Correct option (B)  x - y = 0, (D)  x - 7y = 0

Explanation :

The equation of the circle can be written as

(x - 1/2)² + (y + 3/2)² = 5/2

so that its centre is at (1/2, -3/2) and radius is √5/2. Let y = mx  be the equation of L₁. Since the intercepts are 

made by the circle on L₁ and L₂ , it follows that the two chords are equidistant from the centre. Therefore

m = 1, -1/7

Hence, the equations of L₁ are y = -x /7 and y = -x/7. That is, x - y = 0 and x + 7y = 0