Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 64

The tangent line is horizontal at the point $(7,-16)$. The tangent line is vertical at the point $(-9,0)$.

The slope of the tangent line is given by $dy/dx=y'(t)/x'(t)=(2t-8)/(2t)$. The tangent line is horizontal if $dy/dx=0$. Solving for $t$ we get $t=4$. The corresponding point is $c(4)=(7,-16)$. The tangent line is vertical if $dy/dx$ is infinite. This occurs at $t=0$. The corresponding point is $c(0)=(-9,0)$.