The component form of vector w is (2, 6). The question about the ellipse equation seems disconnected, as the provided kinematics equations aren't related to ellipses.
The component form of a vector is obtained by subtracting the initial point coordinates from the terminal point coordinates. For vector w, with an initial point at (-5,-2) and a terminal point at (-3,4), the component form is w = (x2 - x1, y2 - y1), which computes to w = (-3 + 5, 4 + 2) = (2, 6).
Concerning the ellipse equation, there seems to be some confusion as the information provided about the rotational kinematics equations does not directly pertain to ellipses. However, assuming the ellipse question is separate, the standard form for the equation of an ellipse is X2/a2 + Y2/b2 = 1, where 'a' and 'b' represent the lengths of the semi-major and semi-minor axes respectively.