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Q.
The number of points on $x$ -axis which are at a distance $c(c<3)$ from the point $(2,3)$ is
Introduction to Three Dimensional Geometry
Solution:
Let a point on $x$ -axis be $\left(x_{1}, 0\right)$, then its distance from the point $(2,3)=\sqrt{\left(x_{1}-2\right)^{2}+9}=c$
or $\left(x_{1}-2\right)^{2}=c^{2}-9$
$\therefore x_{1}-2=\sqrt{c^{2}-9} .$
But $c< 3 \Rightarrow c^{2}-9< 0$
$\therefore x_{1}$ will be imaginary.