Tangent is drawn to ellipse x 2 /27 + y 2 = 1 at ( 3 3 cos θ , sin θ ) (where θ ∈ ( 0 , π /2 ) ). Then the value of θ such that sum of intercepts on coordinate axes made by this tangent is least is

Question

Tangent is drawn to ellipse x 2 /27 + y 2 = 1 at ( 3 3 ​ cos θ , sin θ ) (where θ ∈ ( 0 , π /2 ) ). Then the value of θ such that sum of intercepts on coordinate axes made by this tangent is least is K π ​ then K =

TestHub · Accepted Answer

27 x 2 ​ + 1 y 2 ​ = 1 , P ( 3 3 ​ cos θ , sin θ ) ​ 27 3 3 ​ cos θ ​ + 1 sin θ y ​ = 1 ​ ​ ​ ​ ​ ​ A ( 27 3 3 ​ cos θ ​ , 0 ) , B = ( 0 , sin θ 1 ​ ) f ( θ ) = 3 3 ​ sec θ + cosec θ f 1 ( θ ) = cos 2 θ 3 3 ​ sin θ ​ − sin 2 θ cos θ ​ = 0 ⇒ tan 3 θ = 3 3 ​ 1 ​ = ( 3 ​ 1 ​ ) 3 θ = 6 π ​

Mathematics - Ellipse Question with Solution | TestHub

Doubts & Discussion