JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    Let P,Q and R be three conformal points on the parabola \[{{y}^{2}}=4ax\]. Then, the correct statement is

    A)  circle circumscribing the \[\Delta PQR\] passes through the vertex of the parabola.

    B)  the algebraic sum of slopes of the tangents at P, Q and R vanishes.

    C)  the algebraic sum of the ordinates of the points P vanishes.

    D)  circumcentre of \[\Delta PQR\] lies on the axis of the parabola.

    Correct Answer: A

    Solution :

    Since, the line \[\frac{x}{e}+\frac{y}{e'}=1\] touches the circle  \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]. \[\therefore \]    \[\frac{1}{\sqrt{\frac{1}{{{e}^{2}}}+\frac{1}{e{{'}^{2}}}}}=2\] \[\Rightarrow \]            \[a=\frac{ee'}{\sqrt{{{e}^{2}}+e{{'}^{2}}}}=2\]        [from Eq. (i)]

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