Question
Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4 x 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 :
JEE Main
Mathematics
Parabola
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2 x^ 2 =3 y
- B. 3 y^ 2 =2 x
- C. 2 y^ 2 =3 x
- D. 3 x^ 2 =2 y
Answer
C. 2 y^ 2 =3 x
Step-by-step solution
y^2 = 4x Locus of mid point of OP M(h, k) h = t^2 2 , k = t k^2 = 2h y^2 = 2x S: y^2 = 2x R(h, k) h = 3t^2 4 , k = 3t 4 t^2 = 8h 3 , t = 4k 3 16k^2 9 = 8h 3 2k^2 = 3h Locus of R : 2y^2 = 3x
Related: Mathematics — Parabola · All PYQ Banks