Manin's conjecture for a singular quartic del Pezzo surface

We prove Manin’s conjecture for a split singular quartic del Pezzo surface with singularity type $2\text{Aone}$ and eight lines. This is achieved by equipping the surface with a conic bundle structure. To handle the sum over the family of conics, we prove a result of independent interest on a certain restricted divisor problem for four binary linear forms.