Let the coordinates of P be (h,k) Let the equation of a tangent from P(h,K) to the circle x2+y2=a2 be y=mx+a√1+m2 since, P(h,K) lies on y=mx+a√1+m2 therefore, k=mh+a√1+m2=(k−mh)2=a2(1+m2) thisis a quadratic equation in m. Let the two roots be m1 and m2, then m1+m2=
2hK
K2−a2
But tan α=m1,tanβ=m2 and it is given that cotα+cotβ=0 ∴