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Question
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
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Solution
Since the point is on the y-axis so, X-coordinate is zero.
Let the point be (0, y)
Its distance from (5, –2) and (–3, 2) are equal
∴ `sqrt((0 -5)^2 + (y+2)^2) = sqrt((0+3)^2 + (y -2)^2)`
⇒ `25 + y^2 + 4y + 4 = 9 + y^2 - 4y + 4 ....["squaring both sides"]`
⇒ `4y + 29 = -4y + 13`
⇒ `4y + 4y = 13 - 29`
⇒`8y = (-16)/(8) = -2`
Thus, the point is (0,-2)
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