Question

How many points are there on the $x-$axis whose distance from the point $(2,3)$ is less than $3$ units ?

Answer 1

Given point (2, 3)

Let point be (x, 0)

$\sqrt{(x-2{)}^2+(3-0{)}^2}<3$

$=\sqrt{(x-2{)}^2+9}<3$

$=(x-2{)}^2+9<9$

$=x^2+4-4x+9<9$

$=x^2-4x+4<0$

$=(x-2{)}^2<0$

Thus there are infinite points.