Analytic geometry

Analytic geometry

1. Rectangular coordinates

   • Division point. Divides a line segment into a given ratio
   • Median. Line segment that joins a vertex of atriangle with the midpoint of it opposite side
   • Abscissa. Horizontal number line, an "x" real number
   • Quadrants. Four regions of the plane

2. The line

   • Slope. The trigonometric tangent of the angle of inclination.
   • Parallel line. Their slope will be the same
   • Perpendicular lines. Their slope is reciprocal and with opposite sign

3. The circle

   • Circle. Geometric place of all the points in the plane that are equidistant from a fixed point
   • Fixed point. The center of the circle
   • Radius. Any line segment whose endpoints are any points of the same and its center

4. The ellipse

   • Conic section. It is a curve of intersection of a plane with a right circular cone of two mantles.
   • Ellipse. Geometric place of all the points in the cartesian plane that the sum of its distance to two fixed points is constant
   • Foci. The point F and F' are the fixed points
   • Focal axis. It is the line that passes through the foci
   • Vertex. Points of intersection of the ellipse with its focal axis
   • Major axis. It is the line segment whose endpoints are the vertex of the ellipse.
   • Lactus rectum. It is the line segment that is perpendicular to the focal axis
   • Minor axis. It is the line segment that passes through the center

5. The parabola

   • Parabola. Geometric place of all the points in the plane
   • Focus. Distance represented by "a" from the vertex
   • Directrix. Distance "-a" from the vertex
   • Focal parameter. Distance from the focus to the directrix, 2a

6. The hyperbola

   • Transverse axis. Line segment that has a lenght of 2a
   • Conjugate axis. Line segment that has a length of 2b
   • Latus rectum. Line segment perpendicular to the transverse axis and that passes through each focus
   • Point a. Represents the distance from the center to the vertex
   • Point b. Distance from the center to any point of the conjugate axis.