The sum of intercepts on the axes of coordinates by any tangent to the curve x+y=2  is

For the curve x+y=2 , the parametric  coordinates are given by x=2cos2θ  and y=2sin2θ  i.e., x=4cos4θ And x=4sin4θ dydx=4×4sin3θ.cosθ4×4cos3θ(−sinθ)=−tan2θ ⇒Eq. of tangenty−4sin4θ=−tan2θ(x−4cos4θ)   ∴ x−intercept=|4cos4θ+4sin4θtan2θ|=4cos2θ  and ∴ y−intercept=|4sin4θ+4sin4θtan2θ|=4sin2θ  Hence, the sum of intercept made on the axes of coordinates is 4cos2θ+4sin2θ=4