Answer:
PpFf and ppff
Explanation:
Gray skin and smoke breathing are recessive traits so to get expressed their recessive alleles should be present in two copies. Thus the parent with gray skin and smoke breathing traits has the genotype ppff.
Parent with purple skin and fire breathing trait can be PPFF, PpFF, PPFf or PpFf. Since they are dominant traits, only one allele is enough to produce the phenotype. However the resultant progeny has all type of trait combinations present. Along with the dominant variants, recessive variants can also be observed. Recessive genotype progeny will only occur when one of the parents is heterozygous since it receives one recessive allele from the homozygous recessive parent and other recessive allele from the heterozygous parent.
Thus, parent with dominant traits has the genotype PpFf.