Q62 / 180 · COMEDK 2012 · Mathematics

A man running a race-course notes that the sum of the distances from the two flag posts from him is always $10 \mathrm{~m}$ and the distance between the flag posts is $8 \mathrm{~m}$. The equations of the path traced by the man is given by

  • A
    $\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$
  • B
    $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$
  • Correct answer
    C
    $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$
  • D
    $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$

Solution

Given that, $S P+S^{\prime} P=10$ $\Rightarrow \quad 2 a=10 \Rightarrow a=5$ and $\quad 2 a e=8$ $a e=4$ $b^{2}=a^{2}\left(1-e^{2}\right)$ $=a^{2}-(a e)^{2}$ $=25-16=9$ Hence, required equation is $$ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 $$

Hence, the correct answer is option: 'C'.

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