Question 11. Plz fast
Q.11. The tangents to x 2 + y 2 = a 2 having inclinations α   a n d   β intersect at P. If c o t α + c o t β = 0 , then the locus of P is
(a) x + y = 0
(b) x - y = 0
(c) xy = 0
(d) xy = 1

Dear Student,
Please find below the solution to the asked query:

We havex2+y2=a2Let Ph,k is point P Equation of tangent of slope m to circle isy=mx+a1+m2Tangent passes through h,kk=mh+a1+m2k-mh2=a21+m2k2+m2h2-2mhk-a2-a2m2=0m2h2-a2-2khm+k2-a2=0If two roots are m1 and m2 m1+m2=2khh2-a2As per question m1=tanα and m2=tanβGiven thatcotα+cotβ=0cotα=-cotβ1tanα=-1tanβtanα=-tanβtanα+tanβ=0 m1+m2=02khh2-a2=0hk=0xy=0

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