A rectangle PQRS has its side PQ parallel to the line y=mx and vertices P,Q and S on the lines y= a x = b,x = - b respectively. Find the locus of the vertex R.
Please reply with explanation..
Let P (p,a), Q (b,q), R(x,y), S (-b,r).
Midpoint of QS has x coordinate (b-b)/2=0. This means p=-x.
Slope of PQ=(q-a)/(b+x)=m
Slope of QR=(y-q)/(x-b)=-1/m
From above two q can be emilinated and y can be found in terms of x.
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