Midterm Reviewer - Pre Calculus

Studied by 13 people
0.0(0)
Get a hint
Hint

Conic Section

1 / 45

Earn XP

Description and Tags

46 Terms

1

Conic Section

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

New cards
2

Non-degenerate Conics

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

New cards
3

Circle

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

New cards
4

Parabola

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

New cards
5

Ellipse

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

New cards
6

Hyperbola

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

New cards
7

Degenerate Conics

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

New cards
8

Point

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

New cards
9

Line

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

New cards
10

Two intersecting lines

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

New cards
11

General Form of Non-degenerate Conics

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

New cards
12

Circle Coefficient

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

New cards
13

Parabola Coefficient

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

New cards
14

Ellipse Coefficient

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

New cards
15

Hyperbola Coefficient

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

New cards
16

Circle

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

New cards
17

Arc

A portion of the circumference of a circle.

New cards
18

Chord

A line segment connecting two points on a circle.

New cards
19

Diameter

A chord that passes through the center of a circle.

New cards
20

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

New cards
21

Secant Line

A straight line that intersects a circle in two points.

New cards
22

Tangent Line

A line that touches a circle at a single point.

New cards
23

Sector

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

New cards
24

Equations of a Circle

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

New cards
25

Parabola

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

New cards
26

Focus

A fixed point on a parabola.

New cards
27

Directrix

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

New cards
28

Axis of Symmetry

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

New cards
29

Latus Rectum

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

New cards
30

Equations of a Parabola

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

New cards
31

Ellipse

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

New cards
32

Foci

Two fixed points on an ellipse.

New cards
33

Center

The midpoint of the foci of an ellipse.

New cards
34

Major Axis

The longest diameter of an ellipse passing through the foci.

New cards
35

Minor Axis

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

New cards
36

Semi-major Axis

Half of the major axis of an ellipse.

New cards
37

Semi-minor Axis

Half of the minor axis of an ellipse.

New cards
38

Equations of Ellipse

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

New cards
39

Hyperbola

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

New cards
40

Branches

The separate curves that form a hyperbola.

New cards
41

Vertices

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

New cards
42

Center

The midpoint between the vertices of a hyperbola.

New cards
43

Asymptotes

Lines that a hyperbola approaches as it heads towards infinity.

New cards
44

Transverse Axis

The line segment formed by the vertices of a hyperbola.

New cards
45

Conjugate Axis

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

New cards
46

undefined

New cards

Explore top notes

Note
Studied by 10 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 23 people
Updated ... ago
5.0 Stars(3)
Note
Studied by 2 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 6 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 2 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 93 people
Updated ... ago
5.0 Stars(2)
Note
Studied by 11 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 549 people
Updated ... ago
4.0 Stars(5)

Explore top flashcards

Flashcard33 terms
Studied by 49 people
Updated ... ago
5.0 Stars(1)
Flashcard117 terms
Studied by 11 people
Updated ... ago
5.0 Stars(1)
Flashcard43 terms
Studied by 2 people
Updated ... ago
5.0 Stars(1)
Flashcard26 terms
Studied by 23 people
Updated ... ago
5.0 Stars(1)
Flashcard46 terms
Studied by 59 people
Updated ... ago
5.0 Stars(1)
Flashcard147 terms
Studied by 12 people
Updated ... ago
5.0 Stars(1)
Flashcard40 terms
Studied by 111 people
Updated ... ago
5.0 Stars(2)
Flashcard124 terms
Studied by 67 people
Updated ... ago
5.0 Stars(1)