An arch is in the shape of a parabola It has a span of 126 m

An arch is in the shape of a parabola. It has a span of 126 meters and a maximum height of 9 meters.

Find the equation of the parabola?

Determine the height of the arch 28 meters from the center.

Let the equation of parabola be x^2=-4py

With the top most point be vertex of parabola (0,0)

As the top most point is 9 meter the as defined bottom most point is (0,-9)

The atmost sides are (63,-9) and (-63,-9) and parabola passes through these points

Subsituting any one point 63^2 = -4p(-9)

p = 110.25

Equation of parabola =

x^2 = - 441 y

Height of arch 28 meters from center

At 28 meters width from center

x=28

Y = -28×28/(441)

=-1.777

9-1.777

=7.222m