A bridge is curved such that any point along its curvature has a fixed sum of distance with respect to two fixed points

[answerhappygod]

A bridge is curved such that any point along its curvature has a
fixed sum of distance with
respect to two fixed points directly below the bridge (along a
horizontal surface). The height
of the bridge (at its maximum point) is designated by 65 [m],
while its length (measured from
the left endpoint to the right endpoint) is represented by
87 [m].
a. Suppose that a light ray emanates from the left endpoint,
bounces off the bottom of
the bridge, and is reflected towards the right endpoint. Determine
the minimum
distance that light travels in this manner.
b. Determine the horizontal distance (measured from the left
endpoint) and vertical
distance (measured from the horizontal surface) that the light has
bounced from the
bottom of the bridge.
c. Suppose that an object of mass 220 [kg] goes up the bridge
from the right endpoint, up
to a height defined by 32 (where 32 is measured from the point
halfway between the
horizontal distance between the two endpoints to the point along
the bridge where the
object stopped moving). What is the work done by gravitational
force as the object
moves from the right endpoint to its final height? (Hint: Use
parametric equations to
solve for the line integral).
d. At the height mentioned in the previous condition, determine the
rate of change of the
angle 32.
e. For the figure generated by the midpoint between the two
endpoints of the bridge, the
height defined by 32 and its vertical projection with respect to
the ground, determine
the volume of the solid of revolution formed by rotating the figure
about a vertical
axis located at a distance 85 [m] away from the midpoint of the two
edges.