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JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    If a quadrilateral is formed by four tangents to the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\] is a square, then the area of the square is equal to

    A)  20       

    B)                                     22

    C)  24           

    D)                                     26

    Correct Answer: D

    Solution :

    When the quadrilateral is square, so all the four vertices of square would lie on the director circle of the ellipse. \[\Rightarrow \] Square is inscribed in the circle                         \[{{x}^{2}}+{{y}^{2}}\,={{a}^{2}}+{{b}^{2}}\] \[\therefore \] Area of square \[=2({{a}^{2}}+{{b}^{2}})\,=2(9+4)\] \[=2(13)=26\] (square units)


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