Find a point on the x-axis, which is equidistant from the point (7,6) and (3,4).

Explanation

`:'` For any point lying on `x`-axis, `y=0`
Then let the coordinates of required point be `(x,0)`.
`:'` Distance between the points `(7,6)` and `(x,0)=`Distance between the points `(3,4)` and `(x,0)`
`:. Sqrt((x-7)^(2)+(0-6)^(2))=sqrt((x-3)^(2)+(0-4)^(2))`
`implies *x-7)^(2)+36=(x-3)^(2)+16`
`implies x^(2)-14x+49+26=x^(2)-6x+9+16`
`implies -8x=-60`
`implies2x=15`
`x=(15)/(2)`
Therefore, coordinates of required point `=((15)/(2),0)`