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Question

A bridge is in the shape of a semi-ellipse . It is 400 metres long and has a maximum height of 10 metres at the middle point. The height of the bridge at a point at a distance of 80 metres from one end is

A
4 metres
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B
2 metres
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C
8 metres
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D
91 metres
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Solution

The correct option is C 8 metres
We can see that,
AC=400OA=4002=200
and
OB=10

Hence, a=200;b=10

So, Equation of Ellipse will be x22002+y2102=1

Now, at point P from end A =AP=8
OP=OAPA=20080=120

Now, let point Q be (120,y)

Putting this in Equatio x22002+y2102=1

12022002+y2102=1

925+y2100=1y2=100×1625y2=64

y=8

1101172_1188445_ans_f834727c834741aa8b7845b7a8699f02.png

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