Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$ Enter all possible values of $m,$ separated by commas.
what I did: first simplifies the equation to $x^2/4+y^2/(4/m)=1$, then we can see the Foci is $4-4/m$, plugging into the circle equation since they are tangents plugging in I only get one fraction $1/2$, am incorrect since the questions asks for a list
