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JEE Main & Advanced Mathematics Straight Line Question Bank Slope of line, Equation of line in different forms

  • question_answer
    The triangle PQR is inscribed in the circle \[{{x}^{2}}+{{y}^{2}}=25\]. If Q and R have co-ordinates (3,4) and (? 4, 3) respectively, then \[\angle QPR\] is equal to                                  [IIT Screening 2000]

    A)            \[\frac{\pi }{2}\]                       

    B)            \[\frac{\pi }{3}\]

    C)            \[\frac{\pi }{4}\]                       

    D)            \[\frac{\pi }{6}\]

    Correct Answer: C

    Solution :

               Here the centre \[0\,(0,0)\]. So ?m? of OQ is \[\frac{4}{3}\]and ?m? of OR  is \[\frac{-3}{4}\], \ \[\angle QOR=\frac{\pi }{2}\]            Hence \[\angle QPR=\frac{1}{2}\times \frac{\pi }{2}=\frac{\pi }{4}\].


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