Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.)
$x = 8 + 2 \cos(\theta)$, $y = -7 + \sin(\theta)$
horizontal tangent
smaller y-value
$(x, y) = (8, -2)$
larger y-value
$(x, y) = (8, -1)$
vertical tangent
smaller x-value
$(x, y) = (7, -7)$
larger x-value
$(x, y) = (8, -7)$