An ant is moving around the unit circle in the plane so that its location is given by the parametric equations(cos(t), sin(t)). Assume the distance units in the plane are "feet" and the time units are "seconds". In particular, the ant is initially at the point A=(1,0). A spider is located at the point S=(5,0) on thex-axis. The spider plans to move along the tangential line pictured at a constant rate. Assume the spider starts moving at the same time as the ant. Finally, assume that the spider catches the ant at the tangency point P the second time the ant reaches P.

(a) The coordinates of the tangency pointP=(1

5

,24

5

).

(b) The FIRST time the ant reachesPistan1((24))

seconds.

(c) The SECOND time the ant reachesPis+ tan1((24))

seconds.

(d) The parametric equations for the motion of the spider are:

x(t)=524

5

t

+tan1(((24)))

t +tan1((24))

;

y(t)=24

5

t +5tan1(((24)))