JEE AdvancedHardQuestion 300013
Question
If a variable line has x-intercept 'a' and y-intercept 'b' with a + b = 5, the locus of midpoint of the intercept between the axes is:
- Ax + y = 5/2Correct
- B2x + 2y = 5
- Cx/a + y/b = 1
- Dx + y = 5
Correct answer
x + y = 5/2
Explanation
Midpoint of segment between intercepts (a, 0) and (0, b): M = (a/2, b/2). Let h = a/2, k = b/2 → a = 2h, b = 2k. Constraint: a+b = 5 → 2h+2k = 5 → h+k = 5/2. Locus: x + y = 5/2.