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 80 ,highest point at 60 m above the centre.Where should a senator stand to hear the whisper?

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Solution

Now for above elliptical done,
a = 40
b = 60
$e = \sqrt{1 - \frac{{(40)}^{2}}{{(60)}^{2}}}$
$e = \sqrt{\frac{2000}{3600}} \Rightarrow e = \frac{\sqrt{5}}{3}$
Hence, ae = $\frac{40 \sqrt{5}}{3}$
So, senator should stand $\frac{40 \sqrt{5}}{3} m$ from centre

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Q. 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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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 80 ,highest point at 60 m above the centre.Where should a senator stand to hear the whisper?

Now for above elliptical done, a = 40 b = 60 e= ⎷1−(40)2(60)2 e=√20003600⇒e=√53Hence, ae = 40√53So, senator should stand 40√53m from centre

Now for above elliptical done,
a = 40
b = 60
$e = \sqrt{1 - \frac{{(40)}^{2}}{{(60)}^{2}}}$
$e = \sqrt{\frac{2000}{3600}} \Rightarrow e = \frac{\sqrt{5}}{3}$
Hence, ae = $\frac{40 \sqrt{5}}{3}$
So, senator should stand $\frac{40 \sqrt{5}}{3} m$ from centre