​ Let a tangent be drawn to the ellipse x^2/27 + y^2 at (3√3 cos θ, sin θ) where θ ∈ (0, π/2 ). ​

Question

Let a tangent be drawn to the ellipse \(\frac{x^2}{27}+y^2=1\) at (3√3 cos θ,sin θ) where θ ∈ (0, \(\frac{\pi}2\)). Then the value of θ such that the sum of intercepts on axes made by this tangent is minimum is equal to :

(1) \(\frac{\pi}8\)

(2) \(\frac{\pi}4\)

(3) \(\frac{\pi}6\)

(4) \(\frac{\pi}3\)

Answer 1

Correct option is (3) \(\frac{\pi}6\)

Equation of tangent be