Question

Open in App

Verified by Toppr

$PA+PB=10.$

We know that " If a point moves in a plane in such a way that the sum of its distance from two fixed points is constant then the path is an ellipse and this constant value is equal the length of the major axis of the ellipse".

Therefore, the path traced by the man is an ellipse.

Length of the major axis $=10m$

Points $A$ and $B$ are the foci.

Taking the origin of the coordinate plane as the centre of the ellipse while taking the major axis along the $x$-axis the ellipse.

The equation of then ellipse will be of the form $a_{2}x_{2} +b_{2}y_{2} =1$ where $a$ is the semi-major axis.

$2a=10$

The equation of then ellipse will be of the form $a_{2}x_{2} +b_{2}y_{2} =1$ where $a$ is the semi-major axis.

$2a=10$

$⇒a=5$

Distance between the foci $(2c)=8$

$⇒c=ae=4$

Distance between the foci $(2c)=8$

$⇒c=ae=4$

Since, $c=a_{2}−b_{2} $, we get

$4=25−b_{2} $

$⇒16=25−b_{2}$

$⇒b_{2}=25−16=9$

$⇒b=3$

So, the equation of the path traced by the man is $25x_{2} +9y_{2} =1$

0

0