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BCECE Engineering BCECE Engineering Solved Paper-2004

  • question_answer
    If P is any point on the ellipse \[81{{x}^{2}}+144{{y}^{2}}-1944\] whose foci are S and S. Then \[SP+SP\] equals:

    A)  3                            

    B)        \[4\sqrt{6}\]      

    C)         36                         

    D)         324

    Correct Answer: B

    Solution :

    Given equation of ellipse is \[81{{x}^{2}}+144{{y}^{2}}=1944\] \[\Rightarrow \]               \[\frac{{{x}^{2}}}{24}+\frac{{{y}^{2}}}{13.5}=1\] Here, \[{{a}^{2}}=24,\,{{b}^{2}}=13.5\]  \[(\because \,a>b)\] We know that, if P is any point on the ellipse. Then \[SP+SP=2a\] \[\Rightarrow \]               \[SP+SP=4\sqrt{6}\]       \[[\because \,a=2\sqrt{6}]\] Note: If P is any point on the ellipse, then the sum of their distance (SP + SP) is equal to the major axis of the ellipse.


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