Question

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

Answer 1

Given: PA = PB

To Prove: 3x = 2y

Proof: Since PA = PB

So, according to the distance formula,

`=> sqrt((x-5)^2 + (y - 1)^2) = sqrt((x+1)^2 + (y - 5)^2)`

⇒(x−5)² + (y−1)² = (x+1)² +(y−5)²         (Squaring both sides)

⇒x² − 10x + 25 + y² − 2y + 1 = x² + 2x + 1 + y² − 10y +25

⇒−10x − 2y = 2x − 10y

⇒8y = 12x

⇒3x = 2y

Hence, 3x = 2y.