Question

An arch of a bridge is semi-elliptical with major axis horizontal. If the length of the base is \(9\) m and the highest part of the bridge is \(3\) m from the centre of the horizontal axis, the best approximation of the height of the arch \(2\) m from the centre of the base is:

• A. \(11/4\,\text{m}\)
• B. \(8/3\,\text{m}\)
• C. \(7/2\,\text{m}\)
• D. \(2\,\text{m}\)

Hint:

For semi-elliptical arches, use standard ellipse equation.

Answer 1

The Correct Option is A

Step 1: Equation of ellipse: \[ \frac{x^2}{(9/2)^2}+\frac{y^2}{3^2}=1 \]
Step 2: Substitute \(x=2\) and solve for \(y\).
Step 3: \[ y\approx \frac{11}{4}\,\text{m} \]