The locus of the midpoint of the portion of the line xcosα+ysinα=p  intercepted between the axes is

given line is xcosα+ysinα=p xcosαp+ysinαp=1 xpcosα+ypsinα=1A=(pcosα,0) B=(0,psinα)                        Let the point be ∴(h,k)=(p2cosα,p2sinα)  ∴p24h2+p24k2=1Locus is 1x2+1y2=4p2