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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If\[(3,\lambda )\]and (5,6) are the conjugate points of \[{{x}^{2}}+{{y}^{2}}=3,\]then \[\lambda \]is equal to

    A)  2              

    B)  \[-2\]

    C)  1              

    D)  \[-1\]

    Correct Answer: B

    Solution :

     Equation of polar to the circle\[{{x}^{2}}+{{y}^{2}}=3\]at the point\[(3,\lambda )\] \[3x+\lambda y=3\]               ...(i) Since, the points\[(3,\lambda )\]and (5, 6) are conjugate with respect to the circle. \[\therefore \] (5, 6) will satisfy the Eq. (i) \[\therefore \] \[3\times 5+\lambda \times 6=3\] \[\Rightarrow \] \[6\lambda =3-15\] \[\Rightarrow \] \[\lambda =-\frac{12}{6}\] \[\Rightarrow \] \[\lambda =-2\]


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