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)

8/3 m

Answer 2

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)