Question

Find the point on the X-axis, which are at a distance of $2\sqrt{5}$ from the point $(7,-4)$. How many such point are there?

Answer 1

Let the point on the $X$-axis is $(x,0)$

Distance of point $(x,0)$ from point $(7,-4)$ is $\sqrt{(x-7{)}^2+(0+4{)}^2}$

Now,

$\sqrt{(x-7{)}^2+(0+4{)}^2}=2\sqrt{5}$

Square both sides,

$(x-7{)}^2+(4{)}^2=20$

$(x-7{)}^2=20-16$

$(x-7{)}^2=4$

$x-7=\pm 2$

$x=7\pm 2$

$x=9$ or $x=5$

So, the points are $(9,0)$ and $(5,0)$