An arc of a bridge is semi-elliptical with the major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then prove that the best approximation of the height of the acr 2 m from the center of the base is `8/3mdot`

Explanation

Let the eqauation of the semi-elliptical are be
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (ygt0)` ltbrlt Length of the major axis =2a=9
or `a=(9)/(2)`
Lngth of the major semi-minor axis =b=3
So, the equation of the are becomes ltbrlt `(4x^(2))/(81)+(y^(2))/(9)=1`
If x=2, then
`y^(2)=(65)/(9) or y=(1)/(3)sqrt(65)=(8)/(3)` approximately