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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

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    The equations of the tangents of the ellipse \[9{{x}^{2}}+16{{y}^{2}}=144\] which passes through the point (2, 3) is [MP PET 1996]

    A)            \[y=3,\ x+y=5\]                         

    B)            \[y=-3,\ x-y=5\]

    C)            \[y=4,\ x+y=3\]                         

    D)            \[y=-4,\ x-y=3\]

    Correct Answer: A

    Solution :

               The tangent will be \[y-3=m(x-2)\] Þ \[y-mx=3-2m.\]            But it is tangent to the given ellipse, therefore\[m=0,\,-1\]. Hence tangents are \[y=3\]and\[x+y=5\].


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