Question
Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16). If P ( , ) divides this focal chord internally in the ratio 5: 2, then the minimum value of + is equal to :
JEE Main
Mathematics
Parabola
2026
JEE Main 2026 (21 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 16
- B. 5
- C. 7
- D. 22
Answer
C. 7
Step-by-step solution
Parabola y^2 = 16x, a = 4, focus at (4, 0). Point (16, 16) has parameter t_1 = 2. Other end of focal chord: t_2 = -1/t_1 = -1/2, giving (4 1/4, 8 (-1/2)) = (1, -4). P divides the chord in ratio 5:2 internally (two cases): From (16,16) to (1,-4): P = ( 37 7 , 12 7 ), + = 7. From (1,-4) to (16,16): P = ( 82 7 , 72 7 ), + = 22. Minimum value of + = 7.
Related: Mathematics — Parabola · All PYQ Banks