Let required point P(x, y) which is equidistant from the point A(3, 6) and B(-3, 4)
So, PA = PB
⇒ PA2 = PB2
⇒ (x – 3)2 + (y – 6)2 = [x -(-3)]2 + (y – 4)2
⇒ x2 + 9 – 6x + y2 + 36 – 12y = (x + 3)2 + (y – 4)2
⇒ x2 + y2 – 6x – 12y + 45 = x2 + 6x + 9 + y2 + 16 – 8y2
⇒ x2 + y2 – 6x – 12y + 45 = x2 + y2 + 6x – 8y + 25
⇒ -6x – 12y = 6x – 8y + 25 – 45
⇒ -6x – 12y – 6x + 8y = -20
⇒ -12x – 4y = -20
⇒ 3x + y = 5
⇒ 3x + y – 5 = 0