The locus of the point of intersection of two tangents to the ellipse x^2/a^2+y^2/b^2=1 which are inclined at angles θ1,θ2 with the major axis such that cot θ1+cot θ2 is constant=k,isa).2xy=k(x^2-a^2) b.)2xy=k(x^2-b^2) c).2xy=k(y^2-b^2) d). None

Dear Vaibhav

we know that tangent on ellipse is

  y=mx+ √(a²m²+b²)

 simplify it

 m²( x² -a² ) -2mxy + y² -b²=0

m1 +m2  = tanθ1 +tan θ2 = 2xy/(x² -a² )  ...............1

m1.m2 =tanθ1tan θ2 = y² -b²/(x² -a² )......................2

divide 1 and 2

1/ tanθ1 +1/tan θ2 =2xy/y² -b²

k=2xy/y² -b²

2xy =k(y² -b²)

so option c is correct

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