11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer A man running round a race-course notes that the sum of the distance of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 metres. The area of the path he encloses in square metres is  [MNR 1991; UPSEAT 2000]

    A)            \[15\pi \]                                  

    B)            \[12\pi \]

    C)            \[18\pi \]                                  

    D)            \[8\pi \]

    Correct Answer: A

    Solution :

               Here \[2a=10m\]and\[2ae=8m\];  \\[e=\frac{4}{5},\,a=5m\]                   \ \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})=9\]Þ \[b=3\]                    Thus, required area\[=\pi ab=15\pi \,sq.metre\].

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