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Question: M is the middle-point of the line joining (ma, – lb), (mb, – la). P is a variable point on the line...

M is the middle-point of the line joining

(ma, – lb), (mb, – la). P is a variable point on the line

lx + my = n. The loci of the points of trisection of PM are-

A

Independent of a and b

B

Independent of l and m

C

Straight lines which intersect the locus of P at a finite point

D

None of these

Answer

Independent of a and b

Explanation

Solution

Consider two positions P1 and P2 of P. By geometry the points of trisection of MP1 and MP2 should lie on lines parallel to the base P1P2 and this is irrespective of the points with which we start to define the fixed point M.