The co-ordinate axes are rotated about the origin O in the counter-clockwise direction through an angle 60° If p and q are the intercepts made on the new axes by a straight line whose equation referred to original axes is x+y=1, then 1p2+1q2=

If the axes are rotated about the origin in anticlockwise direction, the relations relating old coordinates (x, y) and new coordinates (X, Y) arex=Xcos⁡60∘−Ysin⁡60∘ and y=Xsin⁡60∘+Ycos⁡60∘⇒x=X−3Y2 and y=3X+Y2The equation of the line x + y = 1 with reference to new coordinate axes isX−3Y2+3X−Y2=1⇒(3+1)X+(1−3)Y=2This intercepts lengths p and q on the new-coordinate axes∴ p=23+1 and q=21−3⇒ 1p2+1q2=(3+1)2+(1−3)24=2