Question

The line 3x + 6y = k intersects the curve 2x² + 2xy + 3y² = 1 at points A and B. The circle on AB as diameter passes through the origin. The possible value of k is -

(A)  3

(B)  4

(C)   - 4

(D)  -3

Answer 1

Correct option (A)(D)

Explanation:

Homogenizing (2) with the help of (1), we get

∴ circle described on AB as Diameter passes through (0, 0)

∴ AB will subtend right angle at (0, 0) 

∴ coefficient of x² + coefficient of y² = 0

⇒ (2k 2 -9) + (3k 2 - 36) = 0

⇒k² =  9

⇒ k = ± 3