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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The point of contact of the tangent \[y=x+2\] to the hyperbola \[5{{x}^{2}}-9{{y}^{2}}=45\] is

    A)            (9/2, 5/2)                                  

    B)            (5/2, 9/2)

    C)            (?9/2, ?5/2)                              

    D)            None of these

    Correct Answer: C

    Solution :

               Hyperbola is\[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{5}=1\]. Hence point of contact is \[\left[ \frac{-9(1)}{\sqrt{9-5}},\,\frac{-5}{\sqrt{9-5}} \right]\equiv \left[ \frac{-9}{2},\,\frac{-5}{2} \right]\]. Trick: Since the point \[\left( -\frac{9}{2},\,-\frac{5}{2} \right)\] satisfies both the equations.


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