Conic Sections — Medium JEE math MCQ
**[JEE Mains 2026]** Let one end of a focal chord of the parabola y² = 16x be at point P. If the focus F divides this focal chord internally in the ratio m:n, what is the minimum value of m + n (where m, n are positive integers with gcd(m,n) = 1)?
- A. 2
- B. 3
- C. 4
- D. 5
Solution
For parabola y² = 16x, focus F is at (4, 0).
If P(at², 2at) with a = 4, the other end Q has parameter -1/t.
The focus divides PQ in ratio m:n = t²:1/t² = t⁴:1.
For minimum m + n with gcd = 1: when t = 1, ratio is 1:1.
m + n = 1 + 1 = 2.