"Find the points on the lemniscate "
I found the derivative of the equation, and solved for , getting , but i don't know where to go from here. I was given a couple hints, one of which being "Is the observation helpful? And I don't think it is, but it's obvious where they got it--from
I think you also missed out a power of 2. The equation should beSo, when we differentiate:
and putting gives:
(I think - not )Now we put this back into the original equation, using the hint that :
which you can now solve for , and hence for .