Find points on the curve closest to the origin.

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!

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