2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147169Let 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.14 pages plain TeXAlgebraic Geometrytext