The capitol building in Washington D.C. has elliptical dome.A weak whisper from one focus can be heard clearly at the other focus, but no where else in the room.If length of major axis is 400 feet, highest point at 60 m above the centre.Where should a senator(in m) stand to hear the whisper?

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Solution

400ft = 122m.
Now, a = 61m
b = 60m $e = \sqrt{1 - \frac{3600}{3721}} \Rightarrow e = \sqrt{\frac{121}{3721}} \Rightarrow \frac{11}{61} m$
Now,
ae = $122 \times \frac{11}{61} m \Rightarrow 22 m$
So, Senator should stand 22m from centre.

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The capitol building in Washington D.C. has elliptical dome.A weak whisper from one focus can be heard clearly at the other focus, but no where else in the room.If length of major axis is 400 feet, highest point at 60 m above the centre.Where should a senator(in m) stand to hear the whisper?

400ft = 122m.Now, a = 61m b = 60m e=√1−36003721⇒e=√1213721⇒1161mNow, ae = 122×1161m⇒22mSo, Senator should stand 22m from centre.

400ft = 122m.
Now, a = 61m
b = 60m $e = \sqrt{1 - \frac{3600}{3721}} \Rightarrow e = \sqrt{\frac{121}{3721}} \Rightarrow \frac{11}{61} m$
Now,
ae = $122 \times \frac{11}{61} m \Rightarrow 22 m$
So, Senator should stand 22m from centre.