The correct option (b) 60°
Explanation:
For given ellipse, tangent at point of contact is
[(x cosθ)/a] + [(ysinθ)/b] = 1 .....(1)
also given tangent is (x/a) ∙ (1/2) + (y/b) ∙ (√3/2) = 1 .....(2)
as (1) & (2) are identical
⇒ cos θ = (1/2) and sin θ = (√3/2)
⇒ θ = (π/3) = 60°.