Question

A man running a race-course notes that the sum of the distance from the two flags posts from him is always $10$ metres and the distance between the flag posts is $8$ metres. The equations of the path traced by the man is given by

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

Answer 1

The correct option is C $\frac{x^2}{25}+\frac{y^2}{9}=1$

Since the distance of point from the two fags is constant then locus of points is ellipse.
$SP+S^{1}P=2a$

$\Rightarrow 2a=10$

$\Rightarrow a=5$
$2ae=8$
$ae=4\Rightarrow b^2=a^2(1-e^2)$
$25-16=9=b^2$
$\therefore \frac{x^2}{25}+\frac{y^2}{9}=1$