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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        The equation of the line passing through the centre and bisecting the chord \[7x+y-1=0\] of the ellipse \[{{x}^{2}}+\frac{{{y}^{2}}}{7}=1\]is

    A)  \[x=y\]               

    B)  \[2x=y\]

    C)  \[x=2y\]            

    D)  \[x+y=0\]

    Correct Answer: A

    Solution :

                    Let\[(h,k)\]be the mid-point of the chord \[7x+y-1=0\] Then,     \[\frac{hx}{1}+\frac{ky}{7}=\frac{{{h}^{2}}}{1}+\frac{{{k}^{2}}}{7}\]                         ...(i) and         \[7x+y=1\]                                         ...(ii) represent the same straight line. \[\Rightarrow \]               \[\frac{h}{7}=\frac{k}{7}\] \[\Rightarrow \]               \[h=k\] So, the equation of the line joining (0, 0) and (h, k) is \[y-k=0\].


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