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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The position of the point (1, 3) with respect to the ellipse \[4{{x}^{2}}+9{{y}^{2}}-16x-54y+61=0\]  [MP PET 1991]

    A)            Outside the ellipse                   

    B)            On the ellipse

    C)            On the major axis                     

    D)            On the minor axis

    Correct Answer: C

    Solution :

               \[E\equiv 4+9{{(3)}^{2}}-16(1)-54(3)+61<0\]            Therefore, the point is inside the ellipse.            \[\frac{4{{(x-2)}^{2}}}{36}+\frac{9{{(y-3)}^{2}}}{36}=1\]                    Equation of major axis is \[y-3=0\]and point (1, 3) lies on it.


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