Question

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

Answer 1

Given that the point $P$ is on the $X$-axis.

$\therefore$ its co-ordinates are $P(x,0)$.

Also $P$'s distances $d_1=d_2=d$ from $A(x_1,y_1)=(7,4)=2\sqrt{5}$ units.

$\therefore d=\sqrt{{(x-x_1)}^2+{(y-y_1)}^2}=\sqrt{{(x-7)}^2+{(0-4)}^2}=2\sqrt{5}$

$\Rightarrow x^2-14x+45=0$

$\Rightarrow x=9,5$

Therefore, the co-ordinates of the points on the $X$-axis are $P(9,0)$ and $P(5,0)$.