#### Answer

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

#### Work Step by Step

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 $c(0)=(-9,0)$.