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If the point P(k-1,2) is equidistant fro...

If the point P(k-1,2) is equidistant from the point A(3,k) and B(k,5). Find the value of k ?

Text Solution

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`PA = PB`
`PA^2 = PB^2`
`(k-1-3)^2 + (2-k)^2 = (k-1-k)^2 + (2-5)^2`
`(k-4)^2 + (2-k)^2 = 1+9`
`k^2 - 8k + 16 + 4 - 4k +k^2 = 10`
`2k^2 - 12k + 10 = 0`
`2(k^2 - 6k + 5) = 0`
`2(k-1)(k-5)= 0`
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