Question

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

Answer 1

Let (x, 0) be the point on the x axis. Then as per the question, we have

`⇒ sqrt((x-2)^2 +(0+5)^2) = sqrt((x+2)^2 + (0-9)^2)`

`⇒sqrt((x-2)^2 +(5)^2) = sqrt((x+2)^2+(-9)^2)`

`⇒ (x-2)^2 + (5)^2 = (x+2)^2 +(-9)^2`        (Squaring both sides) 

`⇒ x^2 -4x +4+25=x^2 +4x+4+81`

`⇒ 8x = 25-81`

`⇒x = -56/8=-7`

Hence, the point on the x-axis is (- 7 ,0 ).