+y2=1 Now, equation of tangent to the ellipse at P(3√3cosθ,sinθ) is given by
3√3cosθ⋅x
27
+sinθ⋅y=1 ⇒
xcosθ
3√3
+ysinθ=1⋅⋅⋅⋅⋅⋅⋅(i) X -intercept of Eq. (i) is x=3√3secθ=OA (say) Y -intercept of Eq. (i) is y=cosecθ=OB (say) ∴ Sum of intercepts =3√3secθ+cosecθ=f(θ) (say) ⇒f′(θ)=3√3secθtanθ−cosecθ⋅cotθ Put ⇒
3√3sinθ
cos2θ
=
cosθ
sin2θ
⇒
sinθ
cos2θ
⋅
sin2θ
cos2θ
=
1
3√3
⇒tan3θ=
1
3√3
⇒θ=π∕6 −∞◀
−
────
──|──
θ=π∕6
+
────
▶+∞ ∵f′(θ) changes sign from negative to positive when moving from left to right ∴f(θ) will attain minima at θ=