[Prelim] Pre-Calculus Flashcards

1
Q

Parts of Conic Section:

A
  • Axis
  • Generator
  • Vertex
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2
Q

Types of Conic Sections:

A
  • Circle
  • Parabola
  • Ellipse
  • Hyperbola
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3
Q

Degenerate Conic Sections:

A
  • Point
  • Single Line
  • Pair of interseating Lines
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4
Q

Two millennia ago, Apollonius of Perga, the great Greek geometer,studied the curves formed by the intersection of a plane and a double right circular cone(double-napped circular cone),and discovered many properties of these curves. These curves were later known as ___________.

A

Conic Sections

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5
Q

Two millennia ago, ___________, the great Greek geometer,studied the curves formed by the intersection of a plane and a double right circular cone(double-napped circular cone),and discovered many properties of these curves. These curves were later known as conic sections.

A

Apollonius of Perga

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6
Q

A line perpendicular to the base of the double right circular cone.

A

Axis

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7
Q

A line lying entirely on the cone.

A

Generator

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8
Q

Point of intersection of the two cones.

A

Vertex

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9
Q

Are curves formed by the intersection of a plane and a double-napped circular cone.

A

Conic Section

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10
Q

The plane is perpendicular to the axis.

A

Circle

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11
Q

The plane intersects only one cone; parallel to only one generator.

A

Parabola

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12
Q

The plane is not perpendicular to the axis and is not parallel to any generator or is oblique to the cone’s axis.

A

Ellipse

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13
Q

The plane cuts both halves of the cone or intersects both cones and is parallel to two generators.

A

Hyperbola

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14
Q

Plane cuts the double right circular cone through the vertex only(degenerate ellipse/circle).

A

Point

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15
Q

The cutting plane is parallel to one generator and passes through the vertex.(degenerate parabola)

A

Single Line

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16
Q

The cutting plane is parallel to two generators, cut both halves of the cone,and passes through the vertex.(degenerate hyperbola)

A

Pair of intersecting lines

17
Q

A simple evaluation of an expression called _____________ can easily provide information on the type of conic section.

A

Discriminant

18
Q

The _______ is the distance from the center outwards.

19
Q

The _________ goes straight across the circle, through the center.

20
Q

The ____________ is the distance once around the circle.

A

Circumference

21
Q

Is the shortest word and shortest measure.

22
Q

Is longer

23
Q

Is longest

A

Circumference

24
Q

A line that “just touches” the circle as it passes by is called a ______.

25
A line that cuts the circle at two points is called a _______.
Secant
26
A line segment that goes from one point to another on the circle's circumference is called a _____.
Chord
27
If it passes through the center it is called a _________.
Diameter
28
A part of the circumference is called an ______.
Arc
29
Quarter of a circle is called a _______.
Quadrant
30
Half a circle is called a _________.
Semicircle
31
A set of coplanar points such that the distance from a fixed point is constant.- A set of equidistant points.
Circle
32
A line segment whose endpoints are on a circle.
Chord
33
Twice the size of the radius; cuts the circle into two equal parts, passing through the center.
Diameter
34
A line or plane that touches a curve or other plane at exactly one point (Point of Tangency).
Tangent
35
A line that intersects a circle in two points.
Secant
36
Having the same center.
Concentirc
37
Used to solve for the distance between points
Distance Formula
38
Gives you the coordinates of the center point of a segment.
Midpoint Formula
39
Terms of circle:
- Chord - Diameter - Tangent - Secant - Concentric