Question
If the chord joining the points P _ 1 (x_ 1 , y_ 1 ) and P _ 2 (x_ 2 , y_ 2 ) on the parabola y^ 2 =12 x subtends a right angle at the vertex of the parabola, then x_ 1 x_ 2 -y_ 1 y_ 2 is equal to
JEE Main
Mathematics
Parabola
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 284
- B. 280
- C. 288
- D. 292
Answer
C. 288
Step-by-step solution
Parabola y^2 = 12x has 4a = 12, so a = 3. Parametric points: P_1 = (3t_1^2, 6t_1), P_2 = (3t_2^2, 6t_2). Chord subtends right angle at vertex O(0,0): OP_1 OP_2 = 0. 9t_1^2 t_2^2 + 36t_1 t_2 = 0 t_1 t_2(t_1 t_2 + 4) = 0 t_1 t_2 = -4. x_1 x_2 - y_1 y_2 = 9(t_1 t_2)^2 - 36(t_1 t_2) = 9(16) - 36(-4) = 144 + 144 = 288.
Related: Mathematics — Parabola · All PYQ Banks