The tangents to x2+y2=a2 having inclinations α and β intersect at P. If cot⁡α+cot⁡β=0 then the locus of P is

Let the coordinates of P be (h, k). Let the equation of a tangent from P(h, k) to the circlex2+y2=a2 be y=mx+a1+m2Since P(h, k) lies on y=mx+a1+m2.∴ k=mh+a1+m2⇒ (k−mh)2=a1+m2⇒ m2h2−a2−2mkh+k2−a2=0This is a quadratic in m. Let the two roots bem1 and m2.Then,m1+m2=2hkh2−a2But, tan a= m1 , tan⁡β=m2 and it is given that cot⁡α+cot⁡β=0⇒ 1m1+1m2=0⇒m1+m2=0⇒2hkk2−a2=0⇒hk=0Hence, the locus of (h, k) is xy = 0.