Let and consider the cardioid

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let

a>0

and consider the cardioid

r=a\bigl(1+\cos\theta\bigr)

. What type of tangent line(s) occur at

\theta=\pi

? (a) Vertical only (b) Both horizontal and vertical (c) Horizontal only (d) Oblique with finite, nonzero slope