I'm having some trouble understanding if a parabolic arch problem can be set up the same way as a semiellipse.. for example this problem has me utterly confused:
An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of the second tower. The towers stand 80 inches apart. At a point between the towers and 28 inches along the road from the base of one tower, the cable is 1.44 inches above the roadway. Find the height of the towers.
now this problem, I think I get
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a max height of 35 feet. Find the height of the arch at 25 feet from its center.
the answer I got is about 33.8ft. I set it up as x^2/a^2 + y^2/b^2 = 1. then plugged in the values and solved for y.
is this correct??
I appreciate any and all help