JEE Advanced Model Paper 9 with solutions for online practice

x2 = 16y
Equation of tangent P is x (4t) = 16 (y + t2)/2 is tx = 2y + 2t2
Let tangents cuts x and y axes at A and B respectively. Let A = (2t , 0) and B = (0 , −t2)
Let M (h , k) is the middle point of AB.
h = t , k = −t2 ⇒ h2 = - 2k
Therefore, locus of M (h , k) is x2 + 2y = 0