The locus of the midpoint of the portion between the axes of
xcosα+ysinα=p, where p is a constant, is
1x2+1y2=4p2
The equation of AB isxcosα+ysinα=p⇒xcosαp+ysinαp=1⇒xp/cosα+yp/sinα=1
So the cordinates of A and B are (p/cosα,0) and (0,p/sinα)
therefore, the coordinates of the midpoint of AB are (p2cosα,p2sinα)=(x1,y1)
x1=p2cosα and y1=p2sinα∴cosα=p/2x1 and sinα=p/2y1cos2α+sin2α=1⇒p24(1x21+1y21)=1the locus of (x1,y1) is 1x2+1y2=4p2