Step 1: Identify amino acid \(P\).
The given structure is
\[
\mathrm{HO-C_6H_4-CH_2CH(NH_2)COOH}
\]
which is the structure of the amino acid tyrosine.
Step 2: Identify the hormone derived from tyrosine.
Thyroxine (\(T_4\)) is synthesized from iodinated tyrosine residues and is therefore a derivative of tyrosine.
Step 3: Identify the gland.
Thyroxine is secreted by the
\[
\boxed{\text{Thyroid gland}.}
\]
Step 4: Final conclusion.
Thus,
\[
\boxed{X=\text{Thyroxine},\qquad
Y=\text{Thyroid}}
\]
Hence, the correct option is \(\boxed{(B)}\).