How can I make an EV3 vehicle follow an elliptic equation?
I think it would be more realistic to have the robot drive in a straight line but have a linkage to the foci of the ellipse that "pulls" the robot towards the center of the ellipse just as orbiting objects are pulled toward Earth by gravity.

For example, you could use two nails in a board as the foci. Tie a string in a loop to use as the linkage. Place the string loop around the nails and attach to the side of the robot. Drive the robot forwards (no steering). It will travel in an ellipse. You could even attach a pen to the robot to draw the ellipse.