An ant is moving around the unit circle in the plane so that its location is given by the parametric equations
(
cos
(
π
t
)
,
s
i
n
(
π
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
=
(
10
,
0
)
on the
x
-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) find the coordinates of the tangency point
p
.

(b) the first time the ant reaches
p
is seconds.

(c) the second time the ant reaches
p
is seconds.

(d) find the parametric equations for the motion of the spider.