BITSAT 2014 Paper

Given parabola is y2 = 4x ...(1)
Lt P = (t12,2t1) and Q = (t22,2t2)
Slope of OP =

2t1

t12

=

2

t1

and slope of OQ =

2

t2

Since OP ⊥ OQ,
∴

4

t1t2

= - 1 or t1t2 = - 4 ... (2)
Let R (h, k) be the middle point of PQ, then
h =

t12+t22

2

... (3)
and k = t1+t2 ... (4)
From (4),
k2 = t12+t22+t1t2 = 2h - 8
[ From (2) and (3)]
Hence locus of R (h, k) is y2 = 2x – 8.