Answer
The answer is is $y=-16$.
Work Step by Step
The slope of the tangent line is given by
$dy/dx=y'(t)/x'(t)=(2t-8)/(2t)$.
$\frac{dy}{dx}|_{t=4 }=0$.
Since $c(4)=(7,-16)$, the equation of the tangent line at $t=4$ is
$y+16=0\cdot (x-7)$,
$y=-16$.
