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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,is
a).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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