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Question
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Solution
Let the point on x-axis be P (x,0)
Given ,
PA = PB
PA2 = PB2
(x - 5)2 + (0 - 4)2 = (x + 2)2 + (0 - 3)2
x2 + 25 - 10x + 16 = x2 + 4 + 4x + 9
⇒ - 14 x + 28 = 0
⇒ 14 x = 28
⇒ x = 2
∴ The point on x-axis is (2 , 0)
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