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Find the point on y - axis which is equidistant from point (- 5, - 2) and (3, 2).

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Given points are A(- 5, - 2) and B(3, 2).

We need to find a point on y - axis which is equidistant from these points.

Let us assume the point on y - axis be S(0, y).

We know that distance between the points (x1, y1) and (x2, y2) is

From the problem,

⇒ SA = SB

⇒ SA2 = SB2

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

⇒ (5)2 + (y + 2)2 = (- 3)2 + (y - 2)2

⇒ 25 + y2 + 4y + 4 = 9 + y2 - 4y + 4

⇒ 8y = - 16

⇒ y = -16/8

⇒ y = - 2

∴ The point on y - axis is (0, - 2).

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