Question

Find the points on the y-axis which is equidistant from the points A(6, 5) and B(–4, 3). 

Answer 1

Let P (0, y) be a point on the y-axis. Then as per the question, we have

AP=BP

`⇒ sqrt((0-6)^2 +(y-5)^2) = sqrt((0+4)^2 +(y-3)^2)`

`⇒sqrt((6)^2 +(y-5)^2) = sqrt((4)^2 +(y-3)^2)`

`⇒ (6)^2 +(y-5)^2 = (4)^2 +(y-3)^2`              (Squaring both sides) 

`⇒ 36+y^2 - 10y +25 = 16+y^2-6y +9`

⇒4y = 36

⇒y = 9

Hence, the point on the y-axis is ( 0,9) .