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

Question

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, 3 3, 9 2, 9, 9 3

MARKS App · Accepted Answer

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

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