I am not able to solve this problem-
Two fixed points A and B are taken on the axes such that
OA = a and OB = h; two variable points A' and B' are taken on the
same axes; find the locus of the intersection of AB' and A'B
(1) when OA' + OB' = OA + OB,
and (2) when 1/OA' - 1/OB' = 1/OA - 1/OB
What I was doing
OA' + OB' = a + b
a- OA' + b - OB' = 0
AA' + BB' = 0
OA' = OA -AA'
= a + BB'
x/(a + BB') +y/b = 1 equation No. 1
OB' = OB - BB'
= b - BB'
x/(a) +y/(b-BB') = 1 equation No. 2
Solving 1 and 2 to eliminate BB' and get a relation of required locus.
But answer is of (i) x+y-a-b=0
Thanx in Advance.