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

If the point P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.

Text Solution

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Given that, `" "PA=PB" "rArr" "PA^(2)=PB^(2)`
`rArr" "(k-1-3)^(2)+(2-k)^(2)=(k-1-k^(2))+(2-5)^(2)`
`rArr" "(k-4)^(2)+(2-k)^(2)=(-1)^(2)+(-3)^(2)`
`rArr" "k^(2)-8k+16+4+k^(2)-4k=1+9`
`rArr" "2k^(2)-12k+10=0`
`rArr" "k^(2)-6k+5=0`
`rArr" "k^(2)-5k-k+5=0`
`rArr" "k(k-5)-1(k-5)=0`
`rArr" "(k-5)(k-1)=0`
`rArr" "k-5=0 " "or " "k-1=0`
`rArr" "k=5 " " or " "k=1`
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