﻿ A straight line segment of length ‘p’ moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2. : Kaysons Education

# A Straight Line Segment Of Length ‘p’ moves With Its Ends On Two Mutually Perpendicular Lines. Find The Locus Of The Point Which Divides The Line In The Ratio 1:2.

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## Question

### Solution

Correct option is

Choose the two mutually perpendicular lines as axes of coordinates.

The straight line segment AB of constant length ‘p’ slides so that A andB move along OX and OY respectively. Let P (x1y1) be a point of ABsuch that

APPB = 1:2 it is required to find the locus of P

At any position of AB, let the intercepts OAOB be ab respectively, so that a2 + b2 = p2

Since AP : PB = 1 : 2, we have

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