Step 1: Understanding the Concept:
A test cross is a genetic cross designed to determine the zygosity of an individual displaying a dominant phenotype.
This is achieved by crossing the individual of unknown genotype with a homozygous recessive individual.
The phenotypic ratio of the resulting progeny reveals the genetic composition of the dominant parent.
Step 2: Detailed Explanation:
Let the dominant allele be represented by $A$ and the recessive allele by $a$.
The homozygous recessive parent must have the genotype $aa$.
If the dominant parent is homozygous dominant ($AA$), the cross ($AA \times aa$) will produce only heterozygous dominant offspring ($Aa$).
In this case, $100\%$ of the progeny will display the dominant phenotype, and none will show the recessive trait.
If the dominant parent is heterozygous dominant ($Aa$), the cross ($Aa \times aa$) will produce two types of gamete combinations: $50\%$ $Aa$ (dominant phenotype) and $50\%$ $aa$ (recessive phenotype).
This $1:1$ ratio means exactly half of the progeny will display the recessive trait.
Therefore, the production of recessive offspring in a $1:1$ ratio confirms that the dominant parent is heterozygous.
Step 3: Final Answer:
The genotype of the dominant parent is heterozygous dominant.
This corresponds to Option (B).