Pre-Calc Quiz 1 Flashcards
Conic Sections & Circles
3-dimensional shape formed by set of line segments connecting to a common point.
Cone
The common point that the set of line segments of a cone connects at.
Apex or Vertex
Distance from vertex of a cone to its flat base is the _____
Height of the cone
Its ____ is the segment joining the vertex and the center of the circular base.
Axis
Two types of cones
Right Circular Cone and Oblique Cone
Cone which has a circular base and the axis is perpendicular with the base of the cone.
Right Circular Cone
A cone of which the axis is not perpendicular with its base.
Oblique Cone
Geometric figure made up of two right circular cones with a common vertex or apex.
Double Right Circular Cone
Intersection of a plane and a double right circular cone.
Conic Section or Conic
Line lying entirely on the cone.
Generator
Where do all generators of a cone pass through
Vertex
The only point where the two nappes of the DRCC intersect.
Vertex
Two types of conics
Degenerate and Non-Degenerate
A point, a line, or two intersecting line. Formed when a plane intersects DRCC passing the vertex.
Degenerate Conic
This is a conic, either a parabola, an ellipse, or a hyperbola.
Non-Degenerate Conic
If the cutting plane is parallel to one and only one generator, the curve of intersection is a _____
Parabola
If the cutting plane is not parallel to any generator BECAUSE it cuts all generators, the curve of intersection is ________
Ellipse
If the cutting plane is parallel to the base of the cone, the curve of intersection is _____
Circle
If the cutting plane is parallel to two generators, the curve of intersection is ______
Hyperbola
It is formed when the plane not passing through the vertex is horizontal.
Circle
It is formed when the plane intersects only one cone to form an unbounded curve.
Parabola
It is formed when the intersecting plane intersects only one cone to form a bounded curve.
Ellipse
It is formed when the plane intersects both cones forming two unbounded curves.
Hyperbola
This consists of all points that are at a fixed distance r from a fixed point C.
Circle
What is the fixed distance r of a circle?
Radius
What is the fixed point C of a circle?
Center
Formula when the Center is at origin, or (0,0).
x^2 + y^2 = r^2
What form is x^2 + y^2 = r^2?
Center-Radius Form Equation of a Circle with Center at (0,0)
What is the equation x^2 + y^2 = 1 called?
Unit Circle
What form is (x-h)^2 + (y-k)^2 = r^2
Center-Radius Form Equation of a Circle with Center at (h,k)
