Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Preliminary Questions - Page 602: 5

See the details below.

(a) We can see that in the path $c_1(t)=(f(t),f(t))$, $x=y$. That is, the path is a straight line in the plane, making an angle $\pi/4$ with the $x$-axis. (b) the path will be the same as in $a$, except that in this case $c_2(t)=(f(2t),f(2t))$, so the ant goes faster.