Question

A man running on a race course notes that sum of its distances from two flags posts from him is always 10m and the distance between the flag posts is 8m. He notes that he can read the messages of value system 'HONESTY'and 'RESPECT FOR OTHER'on the poles which ever side he moves. Find the equation of the path traced by the man. Do you think these value systems are necessary in life?

Answer 1

Clearly, path traced by the man will be ellipse.

Given,$SP+S^{\prime }P=10\Rightarrow 2a=10\Rightarrow a=5$

Since, S and S'are focus, i.e. flagposts.

Since, S and S' are (c,0) and $\{c,0\}$and $\{-c,0\}$ respectively.

Therefore, distance between S and S'is

$2c=8\Rightarrow c=4$

Now, we know that

$c^2=a^2-b^2$

$\Rightarrow 16=25-b^2\Rightarrow b^2=9$

$\Rightarrow b=\pm 3$

Hence, equation of ellipse is

$\frac{x^2}{25}+\frac{y^2}{9}=1$

Yes, the given value systems are necessary in life.