JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer     If M is the foot of the perpendicular from a point P oh a parabola to its directrix and SPM is an equilateral triangle, where\[S\]is the focus, then PM is equal to

    A)  \[a\]                                    

    B)  \[2a\]

    C)  \[3a\]                                  

    D)  \[4a\]

    Correct Answer: D

    Solution :

                    Since,\[\Delta SPM\]is an equilateral triangle. Therefore, \[SP=PM=SM\] \[\therefore \]                  \[\angle PMZ=90{}^\circ \] and        \[\angle PMS=60{}^\circ \] \[\therefore \]                  \[\angle SMZ=30{}^\circ \] Now, in right angle\[\Delta SMZ\]                 \[\sin 30{}^\circ =\frac{SZ}{SM}\] \[\Rightarrow \]               \[\frac{1}{2}=\frac{2a}{SM}\] \[\Rightarrow \]               \[SM=4a\] \[\Rightarrow \]               \[PM=4a\]               \[(\because PM=SM)\]

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