Consider an object moving in the plane whose location at timetseconds is given by the parametric equations: x(t)=5cos(t) y(t)=2sin(t). Assume the distance units in the plane are meters.

(a) The object is moving around an ellipse with equation: (x²/b²)+(y²/b²)=1

where a=? and b=? (b) The location of the object at timet=1/3seconds is (?,?) (c) The horizontal velocity of the object at timetisx ' (t)= ? m/s. (d) The horizontal velocity of the object at timet=1/3seconds is ? m/s. (e) The vertical velocity of the object at timetisy ' (t)= ? m/s. (f) The vertical velocity of the object at timet=1/3seconds is ? m/s. (g) The slope of the tangent line at timet=1/3seconds is? (h) Recall, the speed of the object at timetis given by the equation: s(t)=[x'(t)]²+ [y' (t)]²m/s. The speed of the object at timet=1/3seconds is? (i) The first time when the horizontal and vertical velocities are equal is timet=? (j) LetQbe the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse atQis ?