Question

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

Answer 1

Let the coordinates of B be (b, α) and that of S be ( -b, β). Suppose, PR and SQ meet in G. Since, G is mid point of SQ. its, x-coordinates must be 0. Let the coordinates of -R be (h, k). 

Since, G is mid point of PR, the x coordinate of P must be -h. And as P lies on the line y = a, the coordinates of P are (-h, a). Since, PQ is parallel to y = mx, slope of PQ = m

From Eqs. (iii) and (iv), we get