The line x+y = 1 cuts the coordinate axes at P and Q and a line perpendicular to it meet the axes in R and S. The equation to the locus of the point of intersection of the lines PS and QR is

The line x+y=1 meets the coordinate axes at P(1, 0), Q(0, 1) P and S are on y-axis ,Q and R are on x-axisThen the point of intersection is origin ( given they are perpendicular)hence P and Q become the ends of diameter (angle in a semi circle is right angle)∴(x−1)(x−0)+(y−0)(y−1)=0⇒x2+y2−x−y=0