[Prelim] Xy Calculus Flashcards
Curves formed by the intersection of a plane and a double napped circular cone
CONIC SECTIONS
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
The plane is perpendicular to the axis.
CIRCLE
The plane intersects only one cone; parallel to only one generator
PARABOLA
- Formed when the plane is not perpendicular to the axis and is not parallel to any generator or is oblique to the coneβs axis
- Slightly tilted
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
Itβs a _______________ if it passes through the vortex
Degenerate Conic
- A simple evaluation of an expression
- easily provide information on the type of conic section
DISCRIMINANT
set of coplanar points such that the distance from a fixed point is constant.
Circles
Fixed point on a circle
Center
Distance from the center to any point on the circle
Radius
- A line segment whose endpoints are on a circle.
- You know where it ends
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
- Infinite length
Secant
Having the same center
Concentric
Standard form:
(π₯βh)2+ (π¦βπ)2 = π2
General Form:
π΄π₯2+πΆπ¦2+π·π₯+πΈπ¦ = 0
Used to solve for the distance between points
Distance Formula
Gives you the coordinates of the center point of a segment
Midpoint formula
Parts of the conic section:
Axis
Generator
Vertex
Types of conic sections:
Circle
Parabola
Ellipse
Hyperbola
Degenerate conic section:
Point
Single line
Pair of intersecting lines
Terms/part of circle:
Chord
Diameter
Tangent
Secant
Concentric
