.: Conic: from a geometric place :.
In this section we present some geometric consructions for conics: parabola, ellipse and hiperbola.
To reach each of the conics, click the corresponding title of the sub-sections.
Given a focus F and a corresponding line directrix d, the
parabola defined by F and d is
the geometric place of the points that are equidistant of F and d.
Parabola: {P : ||P-F|| = ||P-d||}, that ||P-d|| = min { ||Q-d|| : Q in d}.
Given two foci F1 and F2 and a positive scalar k (k>=||F1-F2||), the
ellipse defined by F1, F2 and k is
the geometric place of the points P which the sum of the distances from P to F2 and to F2
is exactly k.
Ellipse: {P : ||P-F1|| + ||P-F2|| = k}.
The Hiperbola
Given two foci F1 and F2 and a positive scalar k (k<||F1-F2||), the
hiperbola defined by F1, F2 and k is the
geometric place of the points P which the difference, in absolute value, of the distances from P to F2 and to F2
is exactly k.
Hiperbola: {P : | ||P-F1|| - ||P-F2|| | = k}.