Sum of the intercepts on the co-ordinate axes of any tangent to x+y=a  is:

x+y=a⇒dydx=−yx ∴     Equation of tangent at (x1,y1) isy−y1=−y1x1(x−x1) α= intercept on x− axis =ax1 β= intercept on y− axis =ay1 ∴    α+β=a(x1+y1)=aa=a .