VITEEE 2014 Paper

The sum of ordinates of feet of normals drawn from a point to the parabola, y2 = 4ax is always zero .
Now, as normals at three points P, Q and R of parabola y2 = 4ax meet at (h, k).
⇒ The normals from (h, k) to y2 =4ax meet the parabola at P, Q and R.
⇒ y-coordinate y1,y2,y3 of these points and R will be zero.
⇒ y-coordinate of the centroid of ΔPQR
i.e.

y1+y+y3

3

=

0

3

= 0
∴ centroid lies on y = 0