Question

An arch in the form of a semi ellipse has a span of 10 meters and a central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis.
Clearly you have an ellipse with semi-axes

a = 5
b = 4
So, c=3

The latus rectum is the line perpendicular to the semi-major axis, through a focus.

The semi-latus rectum is b^2/a = 16/5
3.2 m is my final answer.
x^2/25 +y^2/16=1
y=3 given
then x=3.3m

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