# 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