[Prelim] Pre-Calculus Flashcards
Parts of Conic Section:
- Axis
- Generator
- Vertex
Types of Conic Sections:
- Circle
- Parabola
- Ellipse
- Hyperbola
Degenerate Conic Sections:
- Point
- Single Line
- Pair of interseating Lines
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 ___________.
Conic Sections
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.
Apollonius of Perga
A line perpendicular to the base of the double right circular cone.
Axis
A line lying entirely on the cone.
Generator
Point of intersection of the two cones.
Vertex
Are curves formed by the intersection of a plane and a double-napped circular cone.
Conic Section
The plane is perpendicular to the axis.
Circle
The plane intersects only one cone; parallel to only one generator.
Parabola
The plane is not perpendicular to the axis and is not parallel to any generator or is oblique to the cone’s axis.
Ellipse
The plane cuts both halves of the cone or intersects both cones and is parallel to two generators.
Hyperbola
Plane cuts the double right circular cone through the vertex only(degenerate ellipse/circle).
Point
The cutting plane is parallel to one generator and passes through the vertex.(degenerate parabola)
Single Line
The cutting plane is parallel to two generators, cut both halves of the cone,and passes through the vertex.(degenerate hyperbola)
Pair of intersecting lines
A simple evaluation of an expression called _____________ can easily provide information on the type of conic section.
Discriminant
The _______ is the distance from the center outwards.
Radius
The _________ goes straight across the circle, through the center.
Diameter
The ____________ is the distance once around the circle.
Circumference
Is the shortest word and shortest measure.
Radius
Is longer
Diameter
Is longest
Circumference
A line that “just touches” the circle as it passes by is called a ______.
Tangent
A line that cuts the circle at two points is called a _______.
Secant
A line segment that goes from one point to another on the circle’s circumference is called a _____.
Chord
If it passes through the center it is called a _________.
Diameter
A part of the circumference is called an ______.
Arc
Quarter of a circle is called a _______.
Quadrant
Half a circle is called a _________.
Semicircle
A set of coplanar points such that the distance from a fixed point is constant.- A set of equidistant points.
Circle
A line segment whose endpoints are on a circle.
Chord
Twice the size of the radius; cuts the circle into two equal parts, passing through the center.
Diameter
A line or plane that touches a curve or other plane at exactly one point (Point of Tangency).
Tangent
A line that intersects a circle in two points.
Secant
Having the same center.
Concentirc
Used to solve for the distance between points
Distance Formula
Gives you the coordinates of the center point of a segment.
Midpoint Formula
Terms of circle:
- Chord
- Diameter
- Tangent
- Secant
- Concentric
