This is an ideal problem for the use of Lagrange multipliers.
Are you in Calc3 ? If so use Langrange Multipliers if not get back to me
Find points on the curve x^2-xy+y^2=9 closest to and farthest from the origin.
I know the distance of point from the origin is, r = sqrt(x^2 + y^2)
Then I subbed the equation into, r(x) = sqrt(x^2 + [f(x)]^2)
and got 9 = sqrt(x^2 + [x^2-xy+y^2]^2)
and I'd solve it when it = 0 to find max and min distance.
I'm not sure if what I'm doing is right? Any help would be appreciated!