Dear Zamil,

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

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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Anil Pannikar

IIT Bombay