  Planar zeros are studied in the context of the five-point scattering
amplitude for gauge bosons and gravitons. In the case of gauge theories, it is
found that planar zeros are determined by an algebraic curve in the projective
plane spanned by the three stereographic coordinates labelling the direction of
the outgoing momenta. This curve depends on the values of six independent color
structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color
indices, the class of curves obtained gets broader by increasing the rank of
the group. For the five-graviton scattering, on the other hand, we show that
the amplitude vanishes whenever the process is planar, without imposing further
kinematic conditions. A rationale for this result is provided using
color-kinematics duality.
