JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q82

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MathematicsSingle correct+4 / -1Question 82 of 90

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

\dfrac92

3\sqrt3

9\sqrt3

Answer and worked solution

Official answer: D

The tangent at $(3\sqrt3\cos\theta,\sqrt3\sin\theta)$ has intercepts $\frac{3\sqrt3}{\cos\theta}$ and $\frac{\sqrt3}{\sin\theta}$ , so the area is $\frac9{\sin2\theta}\ge9$ .

Topics:Tangents and normals to conics Ellipse

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 82