Question

1. If point P (x, y) is at equal distances from points A (6, 1) and B (1, 6), find the relation between x and y.​

Answer 1

Answer:

Let P(x, y) be equidistant from the points A(7, 1) and B(3, 5).

Given, AP = BP

AP2 = BP2

By distance formula,

(x - 7)2 + (y - 1)2 = (x - 3)2 + (y - 5)2

x2 + 49 - 14x + y2 + 1 - 2y = x2 + 9 - 6x + y2 + 25 - 10y

-7x + 25 - y = -3x + 17 - 5y

-4x + 8 + 4y = 0

x - y = 2