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  4. 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

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Q. 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

BITSATBITSAT 2014

Solution:

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)

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