hello!

When you draw an ellipse, use ellipsemode CENTER.

Then the x,y of the ellipse is the center of the ellipse.
Let radiusX, radiusY be the 2 radius of the ellipse.

Then you can say:

1. if ( abs(mouseX-x) < radiusX &&
2.      abs(mouseY-y) < radiusY ) {
3.       // inside
4. }

There are several ways to check it.
Here is one:

1. // Is a point on an ellipse?
2. // http://mathforum.org/library/drmath/view/63045.html
3.  
4. int midX, midY;
5. int sizeX = 500, sizeY = 300;
6. int aSq, bSq;
7.  
8. void setup()
9. {
10.   size(800, 800);
11.   midX = width / 2;
12.   midY = height / 2;
13.   aSq = sizeX * sizeX / 4;
14.   bSq = sizeY * sizeY / 4;
15. }
16.  
17. void draw()
18. {
19.   background(255);
20.   if (inEllipse())
21.   {
22.     fill(#AA5500);
23.   }
24.   else
25.   {
26.     fill(#0055AA);
27.   }
28.   ellipse(midX, midY, sizeX, sizeY);
29. }
30.  
31. boolean inEllipse()
32. {
33.   float xSq = (mouseX - midX) * (mouseX - midX);
34.   float ySq = (mouseY - midY) * (mouseY - midY);
35.   float dist = xSq / aSq + ySq / bSq;
36.   return dist < 1;
37. }