Question

Find the co-ordinate of the point(s) on $x$-axis, which is/are at a distance of $5$ units from the point $(6,-3)$.

• A. $(2,0)$ and $(10,0)$
• B. $(0,2)$ and $(0,10)$
• C. $(2,10)$ and $(0,0)$
• D. None of these

Answer 1

The correct option is A $(2,0)$ and $(10,0)$

Let the co-ordinate of the point on the $x$-axis be $(x,0)$.
$d^2=(x_2-x_1{)}^2+(y_2-y_1{)}^2$
$\Rightarrow 5^2=(x-6{)}^2+(0-(-3){)}^2$
$25=x^2-12x+36+9$
$\Rightarrow x=2$ or $x=10$
So the required points are $(2,0)$ and $(10,0)$