Question

If the distance of P(x, y) from A(6, 2) and B(– 2, 6) are equal prove that y = 2x.

Answer 1

P(x, y), A(6, 2), B(– 2, 6)

PA = PB ⇒ PA^2 = PB^2

(x – 6)^2 + (y – 2)^2 = (x + 2)^2 + (y – 6)^2

⇒ x^2 – 12x + 36 + y^2 – 4y + 4

= x^2 + 4 x + 4 + y^2 – 12y + 36

⇒ – 12x – 4y = 4x – 12y

⇒ 12y – 4y = 4x + 12x

⇒ 8y = 16x

⇒ y = 2x

Answer 2

this is the required answer