A rectangle PQRS has its side PQ parallel to line y=mx and vertices P,Q and S on the lines y=a x=b and x=-b .find locus of vertex R

Question

A rectangle PQRS has  its side PQ parallel to line y=mx and vertices P,Q and S on the lines y=a x=b and x=-b .find locus of vertex R

anonymous · Answer

Hi buddy, 
Use this Method - 
1.A point on a plane if start moving then what is its locus?  
The locus (imagine the point to be alive and start running in all directions ) the path taken by the particle is covering the whole 2D space and hence the locus of the point is whole of 2D space (note here we didnt put any constraint on this point)
A cow tied to a rod with a cord of length 10m , what is the locus of the cow?
Since we are finding the locus of the cow's location the cow can move anywhere in the circle of radius 10m and hence the locus is the complete circle. Here the constraint is that the distance of the cow from the row is always less than 10m.
A point is at a constant distance of R from the origin then find its locus?
The point is at a constant distance from origin hence the locus is the circle of radius R. i.e. $$x^2+y^2=R^2 $$

anonymous · Answer

yup u r rite buddy !ur lucid expanation does deal wid d basis of locus however it is d nature of dis question which sort of baffles me! my assumptions regarding d equations of the lines have been givin me wrong answers.dats d reason y i m lookin forward 2 d exact solution!

anonymous · Answer

a medal plzz