If you have an ellipse like this :
You have the coordinates of your smaller ellipse with this formula :
Example :
float t = 0;
int a = 150;
int b = 100;
void setup(){
size(400,400);
}
void draw(){
background(255);
translate(width/2,height/2);
noFill();
ellipse(0,0,a*2,b*2);
fill(0,0,255);
ellipse(a*cos(t),b*sin(t),10,10);
t += 0.01;
}
You can find further informations on : https://en.wikipedia.org/wiki/Ellipse