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A bridge is in the shape of semi ellipse. It is 400 mts long and has a maximum height 10 mts at the middle point. The height of the bridge at a point distant 80 mts. From one end is

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4 mts

2 mts

8 mts

6 mts

answer is C.

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Detailed Solution

$b = 10, 2 a = 400 \Rightarrow a = 200$

$(120, y) lies on the ellipse \frac{x^{2}}{200^{2}} + \frac{y^{2}}{10^{2}} = 1$

$\frac{120^{2}}{200^{2}} + \frac{y^{2}}{10^{2}} = 1$

$\frac{144}{400} + \frac{y^{2}}{100} = 1$

$\frac{y^{2}}{100} = \frac{456}{400} \Rightarrow y^{2} = \frac{256}{4} \Rightarrow y = 8$

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