WBJEE 2012 Math Solved Paper

According to question, it is given that slope of PX and QX are perpendicular to each other, ie., slope of PX × slope of XQ = - 1
⇒‌

2t

t2

×‌

2m

m2

=−1
⇒‌tm=−4
PQ:‌

x−t2

t2−m2

=‌

y−2t

2t−2m

Let PQ meets axis of parabola Le., x-axis at R(α , 0) then
‌

α−t2

(t+m)(t−m)

=‌

0−2t

2(t−m)

⇒‌α−t2=−t2−tm=−t2+4
⇒‌α=4⇒AR=4