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Avva

Analytic Geometry -----> Ellipse Find the equation of ellipse whose focus is (-1,-1) and the corresponding directrix is x-y+3=0 and e=0.5

  • 2 years ago
  • 2 years ago

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  1. experimentX
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    0.5*(x-y+3)^2/(1+1) = (x+1)^2+(y+1)^2

    • 2 years ago
  2. experimentX
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    solve this, you might get the answer

    • 2 years ago
  3. Avva
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    Thank you for replying me But if you please illustrate what did you do ?? because I can't understand the equation of the given directrix why it has X and Y ??

    • 2 years ago
  4. experimentX
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    x, y is a point on ellipse (x-y+3)^2/(1+1) is the distance from point to directrix so multiply it by eccectricity and on the right hand side you have distance formula .. from foci to point on ellipse hope you understand

    • 2 years ago
  5. ash2326
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    5 minutes

    • 2 years ago
  6. Avva
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    TYT :)

    • 2 years ago
  7. ash2326
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    @Avva do you know what is an ellipse?

    • 2 years ago
  8. ash2326
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    Avva please reply to my question?

    • 2 years ago
  9. Avva
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    am awfully Sorry ash I was away , yes I know an ellipse is a set of points where the sum of distances from a point on it to two fixed points (two foci) is constant = 2a right??

    • 2 years ago
  10. ash2326
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    An ellipse is the set of points in the plane, the sum of whose distance from two fixed points is a given positive constant that is greater than the distance between the two fixed points.

    • 2 years ago
  11. ash2326
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    Here we need a somewhat different definition of ellipse, Are you here?

    • 2 years ago
  12. Avva
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    yes

    • 2 years ago
  13. ash2326
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    Ellipse can also be defined as the locus of points whose distance from a fixed point and a line are in a fixed ratio. The point is one of the focus and the line is the directrix of ellipse. The ratio is the eccentricity of the ellipse

    • 2 years ago
  14. Avva
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    OK , until now I understand both definition

    • 2 years ago
  15. Avva
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    definitions

    • 2 years ago
  16. ash2326
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    Yeah so in our question the focus is -1,1 . and the directrix is x-y+3=0. Let x,y be a point on the ellipse, just use distance formula and tell me its distance from -1,1

    • 2 years ago
  17. Avva
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    \[\sqrt{(x+1)^{2}+(y+1)^{2}}\]

    • 2 years ago
  18. Avva
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    so we will use the formula distance from p(x,y) to the focus (-1,-1) = e*distance from p(x,y) to its directrix Right ??

    • 2 years ago
  19. ash2326
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    Yeah that's right:D

    • 2 years ago
  20. Avva
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    ok Thank You ash for your time and your efforts ,, you have been always my F1 :))

    • 2 years ago
  21. ash2326
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    Welcome @Avva F1???

    • 2 years ago
  22. Avva
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    In any software when you seek help you press F1 :D

    • 2 years ago
  23. ash2326
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    That's creative Avva:)

    • 2 years ago
  24. Avva
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    Thank You ash :) ,, you are brilliant Bro

    • 2 years ago
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