How do I check for collision between an ellipse and a rectangle?

I am working on LibGdx framework for developing a 2D isometric tower defense game.All my sprites are drawn in 2D isometric view.

I have used an array list to store 8 points at boundary in the rectangle.LibGdx has an inbuilt function (returns Boolean) ellipse.contains(x,y),by iterating through array list I can check whether any points are inside ellipse
But the problem is as shown in below picture,it wont detect the enemies in some particular cases

So my question is:
1)Is this a correct approach for solving these kinds of problems
2)If not can you suggest better approach for solving this problem

And I am really sorry for my poor English, I am non native English speaker.

Thank you.