A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

|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.....

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    please anyone, how to solve this ????

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For a circle centered at \[z_0=a+bi\] with radius C the condition must be \[\left|z-z_0\right|=C^2\]

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is value of Z here ...... its ans is " option a" but how to solve this ??

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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...

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This is an ellipse with equation\[\frac{x^2}{5^2}+\frac{y^2}{3^3}=1\]which implies eccentricity of\[e=\sqrt{1-(\frac{3}{5})^2}=\frac{4}{5}\]

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[z=x+iy \rightarrow |z|=\sqrt{x^2+y^2}\]this is what you use to solve this.

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[|z+4|=|(x+iy)+4|=|(x+4)+iy|=\sqrt{(x+4)^2+y^2}\]Similarly with the second magnitude.

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1 Attachment
  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |z+4| is the distance of all z from (-4,0) and |z-4| is the distance of all z from (4,0)

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    as the sum of distances from two fixed points is 10, a constant, thus it is an ellipse

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks Lokisan,conighion, uzma , and what in case of hyperbola .............. lokisan very very thanks, awesome help by u and others

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in case of hyperbola, we take the diffence from two fixed points

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    difference*

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you're welcome

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    From: http://en.wikipedia.org/wiki/Conic_section "Over the complex numbers ellipses and hyperbolas are not distinct"

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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).

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Pretty much. Your finding the locus of points that satisfy the condition you're given.

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    np probs. good luck with it :)

  23. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.