Question

Find that point on x axis which as equidistant from point $(-2,-5)$ and $(2,-3)$

Answer 1

Let the point on the $x-$ axis be $(x,0)$.

$distanceof\left(x,0\right)from(-2,-5)=distanceof\left(x,0\right)from\left(2,-3\right)\Rightarrow \sqrt{{\left(x+2\right)}^2+{\left(0+5\right)}^2}=\sqrt{{\left(x-2\right)}^2+{\left(0+3\right)}^2}\Rightarrow x^2+2x+4+25=x^2-2x+4+9\Rightarrow 4x=9-25=-16\Rightarrow x=-4pointonx-axisis\left(-4,0\right)$