Please help me with this

Question

A parabolic arc is 26 meters across the bottom and 6 m high find the length of the beam that can be installed horizontally across the arc 5 m above the bottom

Answer 1

Here are steps you have to follow:

1. Find equation of the parabola. You can use factored form y=a(x-x_1)(x-x_2) where x_1=0 and x_2=26. So you have y=ax(x-26).To find a you use vertex point (13,6) and plug in the equation. you should get y=-6/169(x)(x-26)
2. Now you have to find points which intersect parabola 5 m above. You can do that by solving 5=-6/169 x(x-26)
3. Using two points you found in step 2, you can now use distance formula to calculate length of beam installed 5 m above