Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4)

Point (x, y) is equidistant from (3, 6) and (- 3, 4)

Therefore,

[(x- 3)² + (y - 6)²]^1/2 = [(x + 3)² + (y- 4)²]^1/2

(x – 3)² + (y – 6)² = (x + 3)² + (y – 4)²

x² + 9 – 6x + y² + 36 – 12y = x² + 9 + 6x + y² + 16 – 8y

36 – 16 = 6x + 6x + 12y – 8y

20 = 12x + 4y

3x + y = 5

3x + y – 5 = 0