This was on last years paper for my upcoming test. My workings got so convoluted that I suspect I have strayed off track. I was wondering if I have overlooked something simple and made it more complicated than it needs to be?

Use implicit differentiation to find the points on the circle closest to and farthest away from the origin.

Taking the derivative I get:

Setting the derivative = 0, I get x = 1 and therefore the top and bottom of the circle: (1,3) and (1,-1)

After graphing the function, I can see that the two points will be where the line y=x intersects the circle.

To find where this happens, I tried to find where the gradient of the circle is perpendicular to that of the line y=x.

:S

So then I tried setting the original equation = y-x

I'm lost on this one :S