Question

In a model, it is shown that an arc of a bridge is semi elliptical with major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal; then the height of the arch, 2m from the centre of the base is (in meters)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the equation of the semi elliptical are be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$(y>0)
Length of the major axis = 2a = 9 $\Rightarrow a=\frac{9}{2}$
So the equation of the arc becomes $\frac{4x^2}{81}+\frac{y^2}{9}=1$
If x=2, then $y^2=\frac{65}{9}\Rightarrow y=\frac{1}{3}\sqrt{65}$