  Let C be a smooth cubic curve in the complex projective plane. We show that
for every positive integer k, there are only finite number of rational curves
of degree k each intersects the cubic C at exactly one point. The number of
such rational curves is known when k is 1, as a smooth cubic has 9 flexes
points. This number seems to be closely related to the number of plane rational
curves of degree k passing through 3k-1 general points, which has been
computed.
