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in Coordinate Geometry by (28.9k points)
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Find a point on y-axis which is equidistant from the points (5, - 2) and (- 3, 2).

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Points A(5, -2) and B(-3, 2) are equidistance from point P. 

Let the coordinates of point are P(0, y) 

Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

⇒ PA = PB

\(\sqrt{(0 - 5)^2 + (y + 2)^2}\) = \(\sqrt{(0 + 3)^2 + (y - 2)^2}\)

On squaring both sides, we get 

(0 - 5)2 + (y + 2)2 = (0 + 3)2 + (y - 2)2 

⇒ (- 5)2 + (y + 2)2 = (3)2 + (y - 2)2 

⇒ 25 + y2 + 4 + 4y = 9 + y2 + 4 – 4y 

⇒ 4y + 4y = 9 – 25 

⇒ 8y = -16 

⇒ y = - 2 

Therefore coordinates are (0, -2).

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