Free JEE Adv 2013 solutions
Take A as ( a, 0) - x axis and B as (0, b ) y axis i.e A is on floor and B is on wall.
Eq of a line from A and B is x/a + y/b = 1
let point x1, y1 divide this line in 2:3 then
x1 = 0+3a/5 and y1 = 2b/5
put value of a , b from above in x/a + y/b = 1
so locus is --- 3x/x1 + 2y/y1 = 5
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