Question

$A(4,0)$ and $B(-4,0)$ are two given points. A variable point P is such that $PA+PB=10$
Show that the equation of locus of P is $\frac{x^2}{25}+\frac{y^2}{9}=1$

Answer 1

$PA+PB=10$

We know that locus of $P$ is an ellipse with $A$ and $B$ as focus

$2a=10$ $2ae=AB=8$

$a=5$ $ae=4$

$e=\frac{4}{5}$ and $b=a\sqrt{1-e^2}=5\times \frac{3}{5}=3$

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