Algebra

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17 Dec 2011 23:11:08 IST
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Complex Numbers
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

What does |z-z1|=k|z-z2| represent?where k is a real no. not equal to 1, z1 and z2 are fixed complex nos., z is moving complex no. and |z| means modulus.



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New kid on the Block

Joined: 10 Sep 2007
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18 Dec 2011 10:48:04 IST
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 circle


Hot goIITian

Joined: 14 Sep 2009
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18 Dec 2011 16:07:13 IST
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How?

New kid on the Block

Joined: 18 Dec 2011
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18 Dec 2011 23:09:14 IST
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haha how mai sab ki baj jati h .. see |z-z1|indicates distanve of z from z1 and similarly for z2.. so its clearly it's a parabola (or hyperbola if k is > 1) as ratio of distance of 2 points from orign is constant (k)
Hari Shankar's Avatar

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20 Dec 2011 15:56:11 IST
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 This is the locus of a circle when k is not 1. Specifically such circles are known as Appollonius circles.

You can read more about them at http://jwilson.coe.uga.edu/emt725/Apollonius/Cir.html




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