Answer
(a) $9$ intersection points.
(b) $9$ intersection points (the same for any value of $c$)
Work Step by Step
(a) We graph the curves for $c=0$ and $c=2$. We notice there are $9$ intersection points.
(b) We graph the curves for $c=5$ and $c=10$. We notice there are the same $9$ intersection points.
