Thread: Solving height of semi elliptical arc

The bridge, in the shape of a semi elliptical arch, has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rect coord system and find the height of the arch at distances of 10, 30, and 50 feet from center.

I believe this would be the equation for the full ellipse:
x^2/60^2 + y^2/25^2 = 1
but don't know what to do beyond that...

How would I go about finding the height at specific distances from center?

Originally Posted by Roxanne4

The bridge, in the shape of a semi elliptical arch, has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rect coord system and find the height of the arch at distances of 10, 30, and 50 feet from center.

I believe this would be the equation for the full ellipse:
x^2/60^2 + y^2/25^2 = 1
but don't know what to do beyond that...

How would I go about finding the height at specific distances from center?

solve for y ... use the (+) solution (upper arch). y = height ... find y(10) , y(30) , etc.

Originally Posted by skeeter

solve for y ... use the (+) solution (upper arch). y = height ... find y(10) , y(30) , etc.

solve for y from the equation I gave?

Originally Posted by Roxanne4

solve for y from the equation I gave?

yes