The squared distance from Y to any point on the ellipse is F jX Yj24 This is a nonnegative periodic and dierentiable function. The major axis of this ellipse is vertical and is the red segment from 2 0 to -2 0. Ev_x aa-bba cos3 t ev_y bb-aab sin3 t This is extremely useful for approximating the ellipse as a circle since we know the centre of curvature for any t.
Ev_x aa-bba cos3 t ev_y bb-aab sin3 t This is extremely useful for approximating the ellipse as a circle since we know the centre of curvature for any t.
The derivation is beyond the scope of this course but the equation is. Recall that when the ellipse is a circle a lies on the line between the circle centre c and p. Squaring and simplifying both sides we get. The formula generally associated with the focus of an ellipse is c 2 a 2 b 2 where c is the distance from the focus to center a is the distance from the center to a vetex and b is the distance from the center to a co-vetex.