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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
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Verified Answer
The correct answer is:
$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$
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
$$
\frac{x^{2}}{25}+\frac{y^{2}}{9}=1
$$
$\Rightarrow \quad 2 a=10 \Rightarrow a=5$
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
$$
\frac{x^{2}}{25}+\frac{y^{2}}{9}=1
$$
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