  Let X be a smooth complete intersection. Suppose p and q are general points
of X, we consider conics in X passing through p and q. We show the moduli space
of these conics is a smooth complete intersection. The main ingredients of the
proof are a criterion for characterizing when a smooth projective variety is a
complete intersection, the Grothendieck-Riemann-Roch theorem and the geometry
of the spaces of conics.
