Find the points on the curve $\displaystyle x^2 + 8xy + 7y^2 = 225$ that are closest to the origin.

Let $\displaystyle D^2=f(x,y)=x^2+y^2$ and $\displaystyle g(x,y)=x^2 + 8xy + 7y^2 - 225$

So: $\displaystyle \triangledown f=\lambda \triangledown g$

gives $\displaystyle \lambda = \frac{x}{x+4y}=\frac{y}{7y+4x} = 4x^2+6xy+4y^2 = 0$

Can somebody do this next step for me or remind what the method is for solving these...