SOLUTION: The gateway Arch in St. louis is parabolic. It is 630 feet high from the ground to the vertex and 630 feet wide on the ground. How high is the focus from the ground?

Question 721202: The gateway Arch in St. louis is parabolic. It is 630 feet high from the ground to the vertex and 630 feet wide on the ground. How high is the focus from the ground?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The gateway Arch in St. louis is parabolic. It is 630 feet high from the ground to the vertex and 630 feet wide on the ground. How high is the focus from the ground?
**
Basic equation of a parabola that opens downwards: (x-h)^2=4p(y-h), (h,k)=(x,y) coordinates of the vertex.
For given problem:
set the origin at 630 ft below the vertex at ground level
vertex: (0,630)
ends of gateway on the ground: (315,0)
2 equations:x^2=4py
axis of symmetry: y-axis or x=0
at vertex:
0=4p*630
at end of gateway:
315^2=0
..
4p*630=315^2
4p=315^2/630
4p=315/2
p=315/8=39.375
focus=(0,590.25) (p-distance below vertex on the axis of symmetry)
How high is the focus from the ground? 590.25 ft

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