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What point on the X-axis is equidistant ...

What point on the X-axis is equidistant from (7, 6) and (-3, 4) ?

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We know that `y`-co-ordinate of a point on X-axis is always 0. So, let a point on X-axis be `P(x, 0)` and let two given points be `A(7, 6) and B(-3, 4).`
According to the condition,
`" "PA=PB`
`rArr" "sqrt((x-7)^(2)+(0-6)^(2))=sqrt((x+3)^(2)+(0-4)^(2))`
Squaring both sides, we have
`" "x^(2)-14x+49 +36=x^(2)+6x+9 +16`
`rArr" "20x=60" "rArr" "x=3`
`therefore` Required point is (3, 0)
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