3
$\begingroup$

Suppose that in the plane a given conic curve is compelled to pass through two fixed points of that plane.

What are the curves covered by a fixed point of the conic, its center (for an ellipse), its focus, etc. ?

(I apologize for the bad English ...)

  • 0
    Your question is ill-posed. To restrict to just only ellipses, for example, one can draw infinitely many ellipses in different orientations that pass through two points.2010-11-22
  • 2
    On the other hand, if you're asking about the locus of a fixed point of a conic of preset type/dimensions constrained to slide on two fixed points, then you have an answerable question...2010-11-22
  • 0
    @J.M. Good distinction. But can't we assume "a given conic curve" means the same thing as "preset type/dimensions" and that only proper Euclidean motions of this curve are contemplated?2010-11-22
  • 0
    Or, perhaps the intent is to fix the *shape* (that is, the *eccentricity*) of the conic, in an investigation of possible generalizations of the observation that "the locus of centers of all circles passing through two points is the perpendicular bisector of the segment joining those points". The locus of foci of co-eccentric conics through two given points contains at least a subset of the perpendicular bisector, via conics with major axes perpendicular to the segment. What pts are added when the conics' axes are allowed to be "skew" to the perpendicular? In particular, what about parabolas?2010-11-22
  • 0
    As OP didn't respond to J. M.'s request for clarification, I vote to close as not a real question2011-04-29

1 Answers 1