the ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio of 1: 2

Dear Paradox

Let coordinate of point be x1,y1 and road is on coordinate axis one end at (x,0) and other end at (0,y) such that x^2+y^2=l^2......................(1)

so applying ratio formula

x1=2x/3

y1=y/3

x=3/2*x1

y=3*y1

putting values of x and y in equation (1)

(3/2*x1)^2+(3*y1)^2=l^2

replace x1,y1 by x,y to get answer.

All the best.

AKASH GOYAL

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Let coordinate of point be x1,y1 and road is on coordinate axis one end at (x,0) and other end at (0,y) such that x^2+y^2=l^2......................(1)so applying ratio formulax1=x/3y1=2y/3x=3x1y=3y1/2putting values of x and y in equation (1)(3/2*x1)^2+(3*y1)^2=l^2replace x1,y1 by x,y => 36x^2+9y^2=4*l^2All the best.