Question

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is $9$ meter and the highest part of the bridge is $3$ meter from the horizontal; the best approximation of the height of the arch. $2$ meter from the centre of the base is

• A. 11/4 m
• B. 8/3 m
• C. 7/2 m
• D. 2 m

Answer 1

Answer: (B)

The equation of the ellipse is
$\frac{x^2}{{\left(\frac{9}{2}\right)}^2}+\frac{y^2}{9}=1$
Where centre is assumed as origin and base as $x$-axis.
Put $x=2$, we get
$\frac{16}{81}+\frac{y^2}{9}=1$
$\Rightarrow y=\frac{\sqrt{65}}{3}\approx \frac{8}{3}m$ (approximately)