Question

The number of points on $x-$axis which are at a distance of $c(c<3)$ units from the point $(2,3)$, is

• A. $0$
• B. $1$
• C. more than $1$ but finite.
• D. infinitely many.

Answer 1

The correct option is A $0$

Let a point on $x$-axis be $(x_1,0)$

Now, the distance from point $(2,3)$
$c=\sqrt{(x_1-2{)}^2+9}\Rightarrow c^2=(x_1-2{)}^2+9$
As $c<3$
$\Rightarrow 0<c^2<9$
$\Rightarrow (x_1-2{)}^2+9<9\Rightarrow (x_1-2{)}^2<0$
which is not possible.

Hence, there are no such points.