Find the linear relation between x and y such that P(x, y) is equidistant from the points A(1, 4) and B(–1, 2).

### Answer

PA = PB

⇒ PA^{2} = PB^{2}

⇒ (x – 1)^{2} + (y – 4)^{2} = (x + 1)^{2} + (y – 2)^{2}

⇒ x^{2} + 1 – 2x + y^{2} + 16 – 8y = x^{2} + 1 + 2x + y^{2} + 4 – 4y

⇒ x + y – 3 = 0