Question

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

Answer 1

Any point on X-axis has co-ordinates of form $(x,0)$
$\therefore (x_1,y_1)=(6,-3)$ and $(x_2,y_2)=(x,0)$ and $d=5$
$\therefore d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$5=\sqrt{(x-6{)}^2+[0-(-3){]}^2}=\sqrt{(x-6{)}^2+3^2}$
Squaring on both sides $5^2(\sqrt{(x-6{)}^2+9}{)}^2$
$25=x^2-12x+36+9$
$x^2-12x+45-25=0\Rightarrow x^2-12x+20=0\Rightarrow (x-10)(x-2)=0$
$\therefore x-10=0$ or $x-2=0\Rightarrow x=10$ or $x=2$
$\therefore$ Required points on X-axis are $(10,0)$ and $(2,0)$