See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

Sol. Equation of tangent having slope m for y2 = 8x is 2 y mx m    m2x – my + 2 = 0 ..... (1) Equation of tangent to the ellipse with parametric angle  is xcos ysin 1 2 k k     ..... (2) For common tangent (1) and (2) are identical  2 cos m k    and 2sin m k    2 cos 4sin k k      2 4sin k 6 cos     , for 2 3    k = 36 57. If two of the three normals drawn from the point (, 0) on the ellipse to the parabola y2 = 8x are perpendicular, then  is equal to _____ Ans.