Analytic Geometry

Vocabulary

asymptote

line that a graph approaches as one of the variables approaches infinity or negative infinity

axis of symmetry

line that divides a graph into two halves that are mirror images

circle

set of all points that are a fixed distance $r$ from a point called the center

co-vertex

one of two points on the ellipse that are endpoints of the minor axis

conic section

resulting cross section when a plane intersects a double cone

conjugate axis

line perpendicular to the transverse axis of a hyperbola and that intersects it at the center of the hyperbola

directrix

line used with the focus to define a parabola. For any point on the parabola, the distance to the focus is equal to the distance to the directrix.

double cone

geometric figure made up of two cones that are opposite each other with their vertices at the same point

ellipse

set of points such that the sum of the distances from two fixed points called the foci remains the same

focus

fixed point used to generate a conic section

fundamental rectangle

rectangle used as a guide to graph a hyperbola. The diagonals of the rectangle are the asymptotes of the hyperbola, and the vertices of the hyperbola are the midpoints of two sides of the rectangle.

hyperbola

set of points such that the difference of the distances from two fixed points called the foci remains the same

major axis

segment that passes through the foci of an ellipse with endpoints on the ellipse

minor axis

segment with endpoints on an ellipse that is perpendicular to the major axis

parabola as a conic section

set of points such that the distance from a fixed point called the focus is equal to the distance to a line called the directrix

distance from the center of a circle to a point on the circle

transverse axis

line that passes through the foci of a hyperbola

vertex of a hyperbola

one of two points where the transverse axis intersects a hyperbola

vertex of a parabola

midpoint of the segment from the focus to the directrix of the parabola

vertex of an ellipse

one of two points on the ellipse that are endpoints of the major axis