Conic Sections !!

           Is called conic section (or just cone) to the intersection of a right circular cone of two sheets with a plane that passes through its apex. They are classified into three types: ellipse, parabola and hyperbola.

          The ellipse is the locus of points in the plane such that the sum of the distances to two fixed points called foci is constant.In addition to the foci F and F 'in an ellipse include the following elements:

 

x^2    +   Y^2

a^2         b^2

         The hyperbola is the locus of the points of difference plane whose distances from two fixed points called foci, is constant and smaller than the distance between spots.

                       Has two asymptotes (straight lines whose distance to the curve tends to zero when the curve moves away to infinity). Hyperbolas whose asymptotes are perpendicular are called equilateral hyperbolas.

In addition to the foci and asymptotes, in the hyperbola are the following elements:

• Central, O
• Vertices, A & A
• Distance between vertices
• Distance between foci

The equation of a hyperbola with center (0, 0), is:

x^2    -   Y^2

a^2         b^2



        The parabola is the locus of points in the plane equidistant from a fixed point called the focus, and a line called the directrix.In addition to the focus, F, and the guideline, d, in a parable include the following elements:

• Axis and
• Vertex, V
• Distance from F to d, p.

Y = ax^2

A parabola, whose apex is at the origin and its axis coincides with the ordinate, is the following equation: