Same here, btw I just discovered this forum, here is the proof I quoted to my friend for i)
"I did some work on Question 16 c
i) x^2 + (y-c)^2 = r^2
And y=x^2
Substitute 2 into 1
y + (y-c)^2= r^2
Rearrange (expand) to make a quadratic, y as the variable
y+y^2 -2yc + c^2 -r^2 = 0...