Question

An arc of a bridge is semi- elliptical with major axis horizontal. The length of the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal. The best approximation of the pillar 2 meter form the center of the base is

• A. $\frac{11}{4}m$
• B. $\frac{8}{3}m$
• C. $\frac{7}{2}m$
• D. $2m$

Answer 1

The correct option is B $\frac{8}{3}m$

R.E.F image

The ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Here $2a=9\Rightarrow a=9/2$ & $b=3$

So, Equation becomes :

$\frac{x^2}{\theta 1/4}+\frac{y^2}{9}=1$

When $x=2$, then

$\frac{4}{\theta 1/4}+\frac{y^2}{9}=1$

$\frac{y^2}{9}=1-\frac{16}{81}=\frac{65}{81}$

$y=\frac{\sqrt{65}}{3}$

So, $y=\frac{8}{3}$ (Approx)