Question
Let A be the focus of the parabola y^ 2 =8 x. Let the line y= m x+ c intersect the parabola at two distinct points B and C. If the centroid of the triangle A B C is ( 7 3 , 4 3 ), then (B C)^ 2 is equal to :
JEE Main
Mathematics
Parabola
2026
JEE Main 2026 (28 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 80
- B. 41
- C. 89
- D. 32
Answer
A. 80
Step-by-step solution
Coordinates of centroid of triangle ABC are 2 3 (t_1^2 + t_2^2 + 1) = 7 3 t_1^2 + t_2^2 = 5 2 4 3 (t_1 + t_2) = 4 3 t_1 + t_2 = 1 (t_1 + t_2)^2 = t_1^2 + t_2^2 + 2t_1 t_2 t_1 t_2 = -3 4 (t_1 - t_2)^2 = (t_1 + t_2)^2 - 4t_1 t_2 = 4 (BC)^2 = 4(t_1^2 - t_2^2)^2 + 16(t_1 - t_2)^2 (BC)^2 = 80
Related: Mathematics — Parabola · All PYQ Banks