### Key Terms

- angle of rotation
- an acute angle formed by a set of axes rotated from the Cartesian plane where, if $\mathrm{cot}\left(2\theta \right)>0,$ then $\theta $ is between $(\mathrm{0\xb0},\mathrm{45\xb0});$ if $\mathrm{cot}(2\theta )<0,$ then $\theta $ is between $(\mathrm{45\xb0},\mathrm{90\xb0});$ and if $\mathrm{cot}\left(2\theta \right)=0,$ then $\theta =\mathrm{45\xb0}$

- center of a hyperbola
- the midpoint of both the transverse and conjugate axes of a hyperbola

- center of an ellipse
- the midpoint of both the major and minor axes

- conic section
- any shape resulting from the intersection of a right circular cone with a plane

- conjugate axis
- the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints

- degenerate conic sections
- any of the possible shapes formed when a plane intersects a double cone through the apex. Types of degenerate conic sections include a point, a line, and intersecting lines.

- directrix
- a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant

- eccentricity
- the ratio of the distances from a point $P$ on the graph to the focus $F$ and to the directrix $D$ represented by $e=\frac{PF}{PD},$ where $e$ is a positive real number

- ellipse
- the set of all points $\left(x,y\right)$ in a plane such that the sum of their distances from two fixed points is a constant

- foci
- plural of focus

- focus (of a parabola)
- a fixed point in the interior of a parabola that lies on the axis of symmetry

- focus (of an ellipse)
- one of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point $\left(x,y\right)$ on the ellipse is a constant

- hyperbola
- the set of all points $\left(x,y\right)$ in a plane such that the difference of the distances between $\left(x,y\right)$ and the foci is a positive constant

- latus rectum
- the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola

- major axis
- the longer of the two axes of an ellipse

- minor axis
- the shorter of the two axes of an ellipse

- nondegenerate conic section
- a shape formed by the intersection of a plane with a double right cone such that the plane does not pass through the apex; nondegenerate conics include circles, ellipses, hyperbolas, and parabolas

- parabola
- the set of all points $\left(x,y\right)$ in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix

- polar equation
- an equation of a curve in polar coordinates $r\phantom{\rule{0.8em}{0ex}}$ and $\theta $

- transverse axis
- the axis of a hyperbola that includes the foci and has the vertices as its endpoints