Question

The point(s) on the $x-$axis which is (are) at a distance of $5$ units from the point $(6,-3),$ is (are)

• A. $(2,0)$
• B. $(10,0)$
• C. $(3,0)$
• D. $(5,0)$

Answer 1

Answer: (A), (B)

The correct options are
A $(2,0)$
B $(10,0)$

Let the point on $x-$axis be $(x,0)$
Now, using distance formula
$5=\sqrt{(x-6{)}^2+(0+3{)}^2}\Rightarrow 5=\sqrt{x^2+36-12x+9}$
Squaring both sides, we get
$25=x^2-12x+45\Rightarrow x^2-12x+20=0\Rightarrow (x-2)(x-10)=0\therefore x=2,10$

Hence, the required points on $x-$axis are $(2,0)$ and $(10,0)$.