BITSAT 2016 Paper

Let the two tangents to the parabola y2=4ax be PT andQT which are at right angle to one another at T(h, k).
Then we have to find the locus of T(h, k).
We know that y=mx+

a

m

,where m is the slope is the equation of tangent to the parabola y2=4ax for all mSince this tangent to the parabola will pass through T(h, k) so
This is a quadratic equation in m so will have two roots,say m1 and m2, then
m1+m2=‌‌

k

h

,‌and‌m1:m2=‌‌

a

h

Given that the two tangents intersect at right angle so
The locus of T(h, k) is x+a=0, which is the equation of directrix.