If the tangent at a point on the ellipse x 2 27 + y 2 3 = 1 meets the coordinate axes at A and B , and O is the origin, then the minimum area (in sq. units) of the triangle O A B is

Step-by-step solution

x 2 27 + y 2 3 = 1 Equation of tangent to ellipse x 27 cos θ + y 3 sin θ = 1 Area bounded by the line and coordinate axis Δ = 1 2 · 27 cos θ · 3 sin θ = 9 sin 2 θ Δ will be minimum when sin 2 θ = 1 Δ min   = 9 sq. units