anonymous
  • anonymous
|z+4| + |Z-4| = 10 is contained or equal to a. ellipse with eccentricity 4/5 b. hyperbola with eccentricity 4/5 c. parabola d. none of these. Where Z is complex Number ????? Pls Help How to Solve These Types Of Question And what are complex number conditions for ellipse, hyperbola, circle, parabola etc.....
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
please anyone, how to solve this ????
anonymous
  • anonymous
For a circle centered at \[z_0=a+bi\] with radius C the condition must be \[\left|z-z_0\right|=C^2\]
anonymous
  • anonymous
what is value of Z here ...... its ans is " option a" but how to solve this ??

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anonymous
  • anonymous
The value of Z is an arbitrary complex number... you need an infinite number of z who satisfy the condition to draw the circle on the complex plain...
anonymous
  • anonymous
This is an ellipse with equation\[\frac{x^2}{5^2}+\frac{y^2}{3^3}=1\]which implies eccentricity of\[e=\sqrt{1-(\frac{3}{5})^2}=\frac{4}{5}\]
anonymous
  • anonymous
\[z=x+iy \rightarrow |z|=\sqrt{x^2+y^2}\]this is what you use to solve this.
anonymous
  • anonymous
\[|z+4|=|(x+iy)+4|=|(x+4)+iy|=\sqrt{(x+4)^2+y^2}\]Similarly with the second magnitude.
anonymous
  • anonymous
by definition, ellipse is the locus of all those points the sum of whose distance from two fixed point is a constant here either u can solve the eq by putting z= x+iy or u can directly find it
anonymous
  • anonymous
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anonymous
  • anonymous
|z+4| is the distance of all z from (-4,0) and |z-4| is the distance of all z from (4,0)
anonymous
  • anonymous
as the sum of distances from two fixed points is 10, a constant, thus it is an ellipse
anonymous
  • anonymous
thanks Lokisan,conighion, uzma , and what in case of hyperbola .............. lokisan very very thanks, awesome help by u and others
anonymous
  • anonymous
in case of hyperbola, we take the diffence from two fixed points
anonymous
  • anonymous
difference*
anonymous
  • anonymous
ok
anonymous
  • anonymous
you're welcome
anonymous
  • anonymous
From: http://en.wikipedia.org/wiki/Conic_section "Over the complex numbers ellipses and hyperbolas are not distinct"
anonymous
  • anonymous
Hyperbolas typically have |f(z)| - |g(z)| = a but you have to check using definitions for z and absolute value, since sometimes you can get degenerate conics from these equations (like straight lines).
anonymous
  • anonymous
so the basic idea is to solve the complex equation and fid the equation and then compare it with the equation of circle ellipse, hyper etc
anonymous
  • anonymous
Pretty much. Your finding the locus of points that satisfy the condition you're given.
anonymous
  • anonymous
k,this question is asked every year in Many Indian Engineering Entrance Exam in different form , thanks all, now i get it, this help me lot.
anonymous
  • anonymous
np probs. good luck with it :)

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