Consider the curve

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

Problem

Consider the curve

r=e^{\theta}

. Which of the following gives the equation of the tangent line at

\theta=a

in point–slope form? (a)

y-e^{a}\sin a=\dfrac{\cos a-\sin a}{\sin a+\cos a}\,(x-e^{a}\cos a)

(b)

y-e^{a}\sin a=e^{a}(\sin a+\cos a)\,(x-e^{a}\cos a)

(c)

y-e^{a}\sin a=\dfrac{\sin a+\cos a}{\cos a-\sin a}\,(x-e^{a}\cos a)

(d)

y-e^{a}\sin a=\dfrac{\sin a-\cos a}{\cos a+\sin a}\,(x-e^{a}\cos a)