maximum no. of rational coordinates on circle whose centre is(1.732,0)i.e.(underroot3,0)is -----------.

Maximum no of rational coordinates will be two.

rCosTheta=-underroot3 for x coordinate to be rational and there are only two such case where circle cuts the Y axis.

 

There cannot be 3 points on the circle with rational coordinates as for then the centre of the circle, being the circumcenter of a triangle whose vertices have rational coordinates must have rational coordinates( since the coordinates will be obtained by solving two linear equations in x, y having rational coordinates) .but the point root3 does not have rational coordinates. also find the equation of the circle is........ For suitable our index, where X is rational, we may have to rational values.