Conics

Conics

1. circumference

   • what is?
     • The circumference is a closed geometric figure whose points are at a constant distance r, called radius, from the center (C).
   • formula
     • The points of the circle (x, y) are those that fulfill the equation:
     • In the particular case of the center circumference (0,0), its equation is given by:

2. elipse

   • parts of elipse
     • The fixed points F1 and F2 are called foci, the focal axis being the line passing through them.
     • The eccentricity of an ellipse is its degree of flattening Cuanto mayor es la excentricidad mas achatada es la elipse
   • what is?
     • An ellipse is a crushed circumference. A circumference has a center, but an ellipse has two foci ("A" and "B" below)

3. parabola

   • what is?
     • A parabola is a curve in which the points are at the same distance from: A fixed point (the focus), and A fixed line (the guideline)
   • Focus and guideline determine how the parable will look
   • parts of parabola
     • Focus: focus F is the fixed point. The points of the parabola are equidistant from the focus and the directive. Guideline: is the fixed line D. The points of the parabola are equidistant from the guideline and the focus. Radius vector: is the segment R that joins the focus with each of the points of the parabola. Axis: is the line E perpendicular to the guideline that passes through the focus.
     • Parameter: is the vector p, that goes from the focus to the nearest point of the guideline Vertices: is the point V of the intersection of the axis and the parabola. Inner and outer points: the parabola divides the plane into two regions. The points that are in the focus region are called inner points (I), while the others are the outer points (J).

4. hyperbola

   • the points of the hyperbola have a property that allows defined as ellugar geometric of the points of the plane whose unlike distances two fixed points (foci) is constant
   • what is?
   • The eccentricity can also be calculated from the semi-axes (a and b) by the formula:

5. what are they?

   • These curves already appeared in the Greek geometry and were denominated conic sections, since the Greeks of the time of Plato considered that these curves came from the intersection of a cone with a plane

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