JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q82

← JEE Main 2014 · 12 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 82 of 90

The minimum area of a triangle formed by any tangent to the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{81}=1$ and the co-ordinate axes is :

Answer and worked solution

Official answer: D

The tangent $\frac{x\cos\theta}4+\frac{y\sin\theta}9=1$ cuts the axes at $\frac4{\cos\theta}$ and $\frac9{\sin\theta}$ .
$\text{Area}=\frac{36}{\sin2\theta}\ge36.$

Topics:Ellipse Tangents and normals to conics

← Previous question Next question →

JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 82