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Ellipse intersect circle

  1. Sep 16, 2010 #1

    Let's say that we have equation of circle as

    x2 + y2 = R2

    and equation of ellipse in quadratic form as

    A x2 + B y2 + Cx + D = 0

    if the circle is inside the ellipse, so there is no intersection ...
    Are x and y imag in this case? /or/ is one of them imag and the other is real ?... etc.
  2. jcsd
  3. Sep 16, 2010 #2


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    No intersection would lead to say 'x' being a complex number.

    So if you sub x=a+bi into any of the equations you will see that x2 gives a complex number as well, which would lead to 'y' being complex as well.
  4. Sep 16, 2010 #3
    Thank you for the reply.

    But 'x' may be real but greater than R which makes 'y' to be pure imaginary.

    So I don't know what is the case that makes 'x' real?
  5. Sep 16, 2010 #4


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    Well if you are plotting on the cartesian plane, then I don't think you would see a geometric reason, if you perhaps plot it on an Argand diagram, you might see a geometric reason.
  6. Sep 16, 2010 #5

    D H

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    Sure it would. Let's look at

    \phantom1 x^2+\phantom1 y^2 &= \phantom1 1 \\
    9x^2 + 4y^2 &= 36

    The solutions (there are four of them) are given by [itex]x^2=32/5[/itex], [itex]y^2=-27/5[/itex]. Note that in this case y is pure imaginary.
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