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# 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

## 2 Answers AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

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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4 years ago
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.

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