Question

The shortest distance of the point $(1,2,3)$ from $x^2+y^2=0$ is

• A. $5$
• B. $\sqrt{5}$
• C. $2$
• D. $\sqrt{14}$

Answer 1

The correct option is B $\sqrt{5}$

$x^2+y^2=0$

$\therefore$ $(x,y)\equiv (0,0)$

Let point be $\equiv (0,0,z)$

$d\equiv \sqrt{{(1-0)}^2+{(2-0)}^2+{(z-3)}^2}=\sqrt{1+4+{(z-3)}^2}\Rightarrow {(z-3)}^2\ge 0$

$d_{min}=\sqrt{5}$