Question

Statement-1 : Any chord of the conic x² + y² + xy = 1, through (0, 0) is bisected at (0, 0) 

Statement-2: The centre of a conic is a point through which every chord is bisected.  

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. 

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True. 

Answer 1

Correct option: (a)

Explanation:

Let y = mx be any chord through (0, 0). This will meet conic at points whose x-coordinates are given by x² + m² x² + mx² = 1 

 ⇒ mid-point of chord is (0, 0) ∀m