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Question
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
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Solution
The given points are A(6,-1) and B(2,3). The point P(x, y) equidistant from the points A and B So, PA = PB
Also,` (PA)^2 = (PB)^2`
`⇒ (6-x)^2 +(-1-y)^2 = (2-x) ^2 +(3-y)^2`
`⇒ x^2-12x +36+y^2+2y+1=x^2-4x+4+y^2-6y+9`
`⇒x^2 +y^2-12 x +2y +37 = x^2 -4x-6y+13`
`⇒ x^2 +y^2 -12x +2y -x^2 -y^2 +4x +6y = 13-37`
⇒ -8x +8y = -24
⇒-8 (x-y) = -24
`⇒x-y =(-24)/(-8)`
`⇒ x-y = 3`
Hence proved
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