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Question
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
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Solution
Let the co-ordinates of the required point on y-axis be P (0, y).
The given points are A (5, 2) and B (-4, 3).
Given, PA = PB
PA2 = PB2
(0 -5)2 + (y -2)2 = (0 + 4)2 + (y - 3)2
25 + y2 + 4 - 4y = 16 + y2 + 9 - 6y
2y = -4
y = -2
Thus, the required point is (0, -2).
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