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Benbotkin
an hourglass is shown next to a paper with the word circle written on it
Circle
A circle is a conic section. It is created by a plane intersecting perpendicular to the cone. It has a center and its boundary is equidistant from the center all the way around.
an object is shown in the diagram and has two lines that are parallel to each other
Ellipse
An ellipse is a conic section. it has two foci that determine the eccentricity, or how wide the ellipse is. It is created by intersecting the cone at an acute angle.
two graphs with the same slope and one point on it, are labeled parabolas
Parabola
A parabola is a conic section. it is created by a plane intersecting the cone at a 45 degree angle. It has one branch that can open up or down.
three different views of the same object, one with an eyeball in it and another with
Focus
Hyperbola and ellipses have two foci, while a parabola has one. It is the point that determines how wide a parabola or hyperbola open, and it determines the eccentricty of an ellipse.
a diagram showing the intersection of two intersecting lines
Asymtotes
Asyptotes are a part of the graph of a hyperbola. There are two for each hyperbola. Each branch of the hyperbola will approach but not cross the asymptotes.
two different types of hypopia are shown in this diagram, one is an x and the other is a cross
Hyperbola
Hyperbola is one of the conic sections. It consists of two branches, with two asymptotes, two vertices, and a center.
an image of a graph paper with two points on it
Vertex
The vertex is the point in a parabola or hyperbola where the graph changes direction. It is the top or bottom of the graph.
three different types of funnels with arrows pointing to the top one and bottom one
Conic Sections
Conic sections are the result of a cone being interseced by planes at various angles. They are a circle, ellipse, hyperbola, and parabola.
an hourglass is shown next to a paper with the word circle written on it
Circle
A circle is a conic section. It is created by a plane intersecting perpendicular to the cone. It has a center and its boundary is equidistant from the center all the way around.
an object is shown in the diagram and has two lines that are parallel to each other
Ellipse
An ellipse is a conic section. it has two foci that determine the eccentricity, or how wide the ellipse is. It is created by intersecting the cone at an acute angle.
two graphs with the same slope and one point on it, are labeled parabolas
Parabola
A parabola is a conic section. it is created by a plane intersecting the cone at a 45 degree angle. It has one branch that can open up or down.
two different types of hypopia are shown in this diagram, one is an x and the other is a cross
Hyperbola
Hyperbola is one of the conic sections. It consists of two branches, with two asymptotes, two vertices, and a center.
two graphs with the same slope and one point on it, are labeled parabolas
Parabola
A parabola is a conic section. it is created by a plane intersecting the cone at a 45 degree angle. It has one branch that can open up or down.
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