Question

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

• A. 2
• B. 1
• C. Infinite
• D. None of these

Answer 1

The correct option is D

None of these

Let a point on x-axis be $(x_1,0)$, then its distance
from the point $(2,3)=\sqrt{(x_1-2{)}^2+9}=c$
or $(x_1-2{)}^2=c^2-9\therefore x_1-2=\sqrt{c^2-9}$
But $c<3\Rightarrow c^2-9<0$
$\therefore x_1$ will be imaginary