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Find the point on "y-a xi s" which is eq...

Find the point on `"y-a xi s"` which is equidistant from the points `(3,1,2)a n d(5,5,2)dot`

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Let point P(0,y,0), on Y-axis is equidistant from A and B.
`therefore PA=PB`
`implies PA^(2)=PB^(2)`
`implies (0-3)^(2)+(y-1)^(2)+(0-2)^(2)`
`=(0-5)^(2)+(y-5)^(2)+(0-2)^(2)`
`implies 9+y^(2)-2y+1+4=25+y^(2)-10y+25+4`
`implies 8y=40`
`implies y=5`
Therefore, the required point is (0,5,0).
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