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Find a point on y-axis which is equid...

Find a point on y-axis which is equidistant from the points `(5,\ -2)` and `(-3,\ 2)` .

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Let the required point on X-axis be P(x,0) and the given points be A (5,-2) and B(-3, 2).
Now, given that
`" "PA=PB" "rArr" "PA^(2)=PB^(2)`
`rArr" "(x-5)^(2)+(0+2)^(2)=(x+3)^(2)+(0-2)^(2)`
`rArr" "x^(2)-10x+25+4=x^(2)+6x+9+4`
`rArr" "-16x=-16" "rArr" "x=1`
`therefore` Required point is (1, 0)
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