See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

For any m  R we have M  N   Which means point (0, c) is on or in the ellipse 2 2 x y 1 4 / 3 4   . Therefore 2 c 1 4   2 c 2   hence correct answer is D Alternative Our aim is find range of c such that intersection. M  N    m  R. Put y = mx + c in ellipse 3x2 + y2 = 4  3x2 + (mx + c)2 – 4 = 0  (3 + m2)x2 + 2mxc + (c2 – 4) = 0 D = B2 – 4AC, D  0 (2mc)2 – 4(3 + m2) (c2 – 4)  0  – 12c2 + 48 + 16m2  0  m  R  – 12c2 + 48  0, c2  4  |c|  2, c [–2, 2] hence correct answer is D.