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