Let and for real numbers

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

Problem

Let

x=\dfrac{2t}{1+t^{2}}

and

y=\dfrac{1-t^{2}}{1+t^{2}}

for real numbers

t

. For which value(s) of

t

does the curve have a vertical tangent line? (a)

t=0

(b)

t=\pm \dfrac{1}{\sqrt{2}}

(c)

t=\pm 1

(d) The curve has no vertical tangent line.