A bridge is in the shape of a semi ellipse. If it is 400m long and has a maximum height of 10m at midpoint. The height of the bridge distanced 80m from one end is

Bridge is in the shape of semi ellipse.

∴b=10, 2a=400⇒a=200
Equation of the ellipse is

$\frac{x^2}{{200}^2}+\frac{y^2}{{10}^2}=1$
Centre of the ellipse is (0,0)
Distance of required point from centre is 200−80=120 m

Let depth of the point is h, then (120,h) lies on the ellipse.

$$\begin{gathered} \frac{{120}^2}{{200}^2}+\frac{h^2}{100}=1 \\ \Rightarrow h^2=64 \\ \Rightarrow h=8 \end{gathered}$$