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1

Conic Section

Curves formed by the intersection of a plane with one or two nappes of a cone.

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Non-degenerate Conics

Circle, parabola, ellipse, and hyperbola formed by the intersection of a plane with a cone.

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3

Circle

A conic section formed when the plane is parallel to the base of the cone.

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4

Parabola

A conic section formed when the plane intersects only one cone to form an unbounded curve.

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5

Ellipse

A conic section formed when the tilted plane intersects only one cone to form a bounded curve.

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6

Hyperbola

A conic section formed when the plane intersects both cones to form an unbounded curve.

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7

Degenerate Conics

Conic sections resulting from a plane intersecting the double cone and passing through the apex.

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8

Point

A degenerate conic section resulting from a plane intersecting the double cone at a single point.

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9

Line

A degenerate conic section resulting from a plane intersecting the double cone in a straight line.

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10

Two intersecting lines

A degenerate conic section resulting from a plane intersecting the double cone in two intersecting lines.

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11

General Form of Non-degenerate Conics

The general form equation for a conic section, where A, B, and C are not all zero.

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12

Circle Coefficient

A circle has A = C ≠ 0 in the general form equation.

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13

Parabola Coefficient

A parabola has AC = 0 in the general form equation.

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Ellipse Coefficient

An ellipse has AC > 0 in the general form equation.

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Hyperbola Coefficient

A hyperbola has AC < 0 in the general form equation.

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16

Circle

A set of all points in a plane equidistant from a fixed point called the center.

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17

Arc

A portion of the circumference of a circle.

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18

Chord

A line segment connecting two points on a circle.

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19

Diameter

A chord that passes through the center of a circle.

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20

Radius

The distance from the center of a circle to any point on its circumference.

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21

Secant Line

A straight line that intersects a circle in two points.

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22

Tangent Line

A line that touches a circle at a single point.

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Sector

The region bounded by an arc of a circle and the two radii to the arc's endpoint.

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24

Equations of a Circle

Equations for a circle with its center at the origin or at (h, k) and its radius r.

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25

Parabola

The locus of all points in the plane whose distances from a fixed point and a fixed line are the same.

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Focus

A fixed point on a parabola.

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Directrix

A fixed line not passing through the focus of a parabola.

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Axis of Symmetry

A line passing through the focus and perpendicular to the directrix of a parabola.

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Latus Rectum

A line segment passing through the focus and perpendicular to the axis of symmetry of a parabola.

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30

Equations of a Parabola

Equations for a parabola with its focus, directrix, and axis of symmetry.

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Ellipse

The set of all points in a plane whose sum of distances from two specific points is a constant.

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Foci

Two fixed points on an ellipse.

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Center

The midpoint of the foci of an ellipse.

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Major Axis

The longest diameter of an ellipse passing through the foci.

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Minor Axis

The shortest diameter of an ellipse perpendicular to the major axis at the center.

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Semi-major Axis

Half of the major axis of an ellipse.

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Semi-minor Axis

Half of the minor axis of an ellipse.

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Equations of Ellipse

Equations for an ellipse with its center at the origin or at (h, k).

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Hyperbola

The set of all points in a plane whose distances from two fixed points have an absolute difference equal to a constant.

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Branches

The separate curves that form a hyperbola.

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Vertices

The points on the separate branches of a hyperbola where the distance is at a minimum.

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Center

The midpoint between the vertices of a hyperbola.

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Asymptotes

Lines that a hyperbola approaches as it heads towards infinity.

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44

Transverse Axis

The line segment formed by the vertices of a hyperbola.

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45

Conjugate Axis

The line segment perpendicular to the transverse axis through the center of a hyperbola.

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46

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