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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    The minimum area of a triangle formed by any tangent to the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{81}=1\] and the coordinate axes is

    A)  26                               

    B)  12

    C)  18                               

    D)  36  

    Correct Answer: D

    Solution :

    \[\Delta =\frac{1}{2}\,\left( \frac{a}{\cos \theta } \right)\,\left( \frac{b}{\cos \theta } \right)\,=\frac{ab}{\sin 2\theta }\ge ab\] \[\therefore \,\,\,\,{{\Delta }_{\min .}}=(4)\,(9)\,=36\]


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