|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.....

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|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.....

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please anyone, how to solve this ????
For a circle centered at \[z_0=a+bi\] with radius C the condition must be \[\left|z-z_0\right|=C^2\]
what is value of Z here ...... its ans is " option a" but how to solve this ??

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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...
This is an ellipse with equation\[\frac{x^2}{5^2}+\frac{y^2}{3^3}=1\]which implies eccentricity of\[e=\sqrt{1-(\frac{3}{5})^2}=\frac{4}{5}\]
\[z=x+iy \rightarrow |z|=\sqrt{x^2+y^2}\]this is what you use to solve this.
\[|z+4|=|(x+iy)+4|=|(x+4)+iy|=\sqrt{(x+4)^2+y^2}\]Similarly with the second magnitude.
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
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|z+4| is the distance of all z from (-4,0) and |z-4| is the distance of all z from (4,0)
as the sum of distances from two fixed points is 10, a constant, thus it is an ellipse
thanks Lokisan,conighion, uzma , and what in case of hyperbola .............. lokisan very very thanks, awesome help by u and others
in case of hyperbola, we take the diffence from two fixed points
difference*
ok
you're welcome
From: http://en.wikipedia.org/wiki/Conic_section "Over the complex numbers ellipses and hyperbolas are not distinct"
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).
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
Pretty much. Your finding the locus of points that satisfy the condition you're given.
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.
np probs. good luck with it :)

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