Attempt:
Given, radius of wheel $0.5 m$
Total distance travelled by the point during first revolution = circumference of the wheel
therefore, distance travelled by the point $2 \pi r$
where r is the radius of the wheel
distance travelled by the point $2 \cdot 3.14 \cdot 0.5 = 3.14 m$
Now, a circle can be defined as the locus of the all points on it that satisfies the equations,
$x = r cos(t), y = rsin(t)$
where x, y are the coordinates of any point on the circle, r is the radius of the circle and t is the parameter - the angle subtended by the point at the circle's center
so the parametrization of the path would be
$x = 0.5cos(t), y = 0.5sin(t)$
Is it right?
That parametrization is with respect to the midpoint of the wheel. But note that the midpoint is moving as well! You'll need to account for that movement, too, see https://en.wikipedia.org/wiki/Cycloid.