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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

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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Badiuddin

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