Question

If the points P (x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x = 2y.

Answer 1

Since P (x, y) is equidistant from A (5, 1) and B (-1, 5), then

PA = PB

or PA² = PB²

(5 – x)² + (1 – y)² = (– 1 – x)² + (5 – y)²

(25 + x² – 10x) + (1 + y² – 2y) = (1 + x² + 2x + 25 + y² – 10y)

26 + x² – 10x + y² – 2y = (26 + x² + 2x + y² – 10y)

12x = 8y

3x = 2y

Hence proved.