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

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#### Solution

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) .

Concept: Coordinate Geometry

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