The curve is given by

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

Problem

x=a t,\;y=t^{2}+1

. If the tangent at

t=2

passes through the point

(5,10)

, the value of the constant

a

is: (a)

\dfrac{5}{2}

(b)

\dfrac{20}{13}

(c)

\dfrac{5}{3}

(d)

\dfrac{15}{8}