Q28 of 77 Page 7


If a point (x, y) is equidistant from (6, -1) and (2, 3), find the relationbetween x and y.


SOLUTION:

Let the points be P(x, y), A(6, -1) and B(2, 3).
AP 2 = (x - 6) 2 + (y + 1) 2
BP 2 = (x - 2) 2 + (y - 3) 2
Given, (x, y) is equidistant from (6, -1) and (2, 3)
(x - 6) 2 + (y + 1) 2 = (x - 2) 2 + (y - 3) 2
⇒ x 2 – 12x + 36 + y 2 + 2y + 1 = x 2 – 4x + 4 + y 2 – 6y + 9
⇒ – 12x + 36 + 2y + 1 = – 4x + 4 – 6y + 9
⇒ – 8x + 8y = -24
⇒ – x + y = -3
⇒ x – y = 3.

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