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JEE Main & Advanced Mathematics Conic Sections Question Bank Mock Test - Conic Sections

  • question_answer
    If the tangents are drawn from any point on the line \[x+y=3\]to the circle \[{{x}^{2}}+{{y}^{2}}=9\], then the chord of contact passes through the point

    A) (3, 5)   

    B) (3, 3)

    C) (5, 3)  

    D) None of these

    Correct Answer: B

    Solution :

    [b] Let (\[(\alpha ,3-\alpha )\]) be any point on \[x+y=3.\] Then, the equation of chord of contact is \[\alpha x+(3-\alpha )y=9\] i.e., \[\alpha (x-y)+3y-9=0\] Therefore, the chord passes though the pint (3, 3) for all values of \[\alpha \].


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