The locus of the point of intersection of the lines xcosα+ysinα=a  and xsinα−ycosα=b  is

Given straight lines are                 xcosα+ysinα=a  …(1)And        xsinα−ycosα=b  …(2) Intersection, we have to eliminate α  between (1) and (2). Squaring (1) and (2) and adding, we get  x2+y2=a2+b2 , which is the equation of a circle.