Question

A point $P$ on $X-$ axis is at distance $13$ from $A(11,12)$. Find the coordinates of $P$.

Answer 1

point P is on X-axis which means its y-coordinate=0

So, P point will be represented as, (x,0)

using distance formula to find the distance between point P and A

$\sqrt{{\left(11-x\right)}^2+{\left(12-0\right)}^2}=13$

${\left(11-x\right)}^2+{12}^2={13}^2$

${\left(11-x\right)}^2={13}^2-{12}^2$

${\left(11-x\right)}^2=25$

$11-x=\pm 5$

$11-x=5or11-x=-5$

$x=6orx=16$

Thus P could be $(6,0)$ or $(16,0)$