Equation of a ellipse x^2+ 4y^2= 4

and equation of a circle = (x+1)^2 + y^2 = 1

At how many points does the graph of circle intersect the graph of the ellipse?

So, if we just solve the algebra we will get that the ellipse and circle share same coordinates with three points. But one of them is certainly the tangency points. And, also the circle can intersect the ellipse at a even number of points. My question is do GRE consider the tangency points as intersection points? should we just find the number of points that both of these figure shares and select that as answer?