Final answer:
The poem known for using an extended metaphor to declare the poet's undying love for his lady is "To His Coy Mistress" by Andrew Marvell, in which the poet elaborates on the theme of seizing the day and the intensity of his love. The correct answer id D.
Step-by-step explanation:
The poem being described as an extended metaphor proclaiming the poet's undying love for his lady is "To His Coy Mistress" by Andrew Marvell. This poem discusses the concept of carpe diem or 'seize the day' and addresses the unlikelihood of protracted courtship in the face of the brevity of life. Marvell uses hyperbolic terms to present the theme of love, such as a love that would grow 'vaster than empires' and the extravagant notion of waiting for the conversion of the Jews. Unlike the other options, "To His Coy Mistress" directly speaks of the poet's love for his mistress.
In contrast, "The Tyger" by William Blake is more about the creation and the creator's power, "Kubla Khan" by Samuel Taylor Coleridge delves into the power of the poet's imagination, and "Ode to a Nightingale" by John Keats reflects on the transience of human life in contrast to the immortality of art and nature. None of these poems have the extended metaphor of undying love seen in Marvell's poem. "The Lady of Shalott" by Alfred Lord Tennyson also does not fit this description, as it is more about the curse and isolation of the Lady than an extended metaphor for love. The correct answer id D.