Question

Find the point on x-axis which is equidistant from the points (2,-5) and (-2,9).

Answer 1

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

Let $A(2,-5)$ and $B(-2,9)$. Then,

$PA=PB$

$P{A}^2=P{B}^2$

$(2-x{)}^2+(-5-0{)}^2=(-2-x{)}^2+(9-0{)}^2$

$4+x^2-4x+25=4+x^2+4x+81$

$-8x=56$

$x=-7$

Therefore, the required point is $(-7,0)$.