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If the Distances of P(X, Y) from A(5, 1) and B(–1, 5) Are Equal, Then Prove that 3x = 2y - CBSE Class 10 - Mathematics

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

⇒x− 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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Solution If the Distances of P(X, Y) from A(5, 1) and B(–1, 5) Are Equal, Then Prove that 3x = 2y Concept: Distance Formula.
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