(4) x = a sinθ – b cosθ --- (i) y = a cosθ + b sinθ --- (ii) On squaring and adding both the equations, x2+y2=(asinθ−bcosθ)2+(acosθ+bsinθ)2 =a2sin2θ+b2cos2θ−2absinθ.cosθ+a2cos2θ+b2sin2θ+2absinθ.cosθ =a2(sin2θ+cos2θ)+b2(cos2θ+.sin2θ) =a2+b2[∵sin2θ+cos2θ=1]