y2=4x
Locus of mid point of OP
M(h,k)⇒h=2t2,k=t
⇒k2=2h⇒y2=2x
S:y2=2x
R(h,k)
⇒h=43t2,k=43t
t2=38h,t=34k
⇒916k2=38h⇒2k2=3h
Locus of R : 2y2=3x
Let the locus of the mid-point of the chord through the origin O of the parabola y2=4x be the curve S. Let P be any point on S. Then the locus of the point, which internally divides OP in the ratio 3:1, is :
Held on 22 Jan 2026 · Verified 6 Jul 2026.
2x2=3y
3y2=2x
2y2=3x
3x2=2y
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