Overview: What Is a Conic Section?
Conic sections are the curves formed when a right circular cone intersects with a plane. The angle that the plane makes when it “cuts through” the cone determines the shape of the section. The four main types of conic sections are the circle, the parabola, the hyperbola, and the ellipse.
The Circle Has One Fixed Center Point
The circle is the curve that is formed when the plane that intersects the cone is perpendicular to the axis of the cone. In other words, the plane cuts though the cone at a 900 angle. The radius is exactly the same distance from the center all along the curve. Therefore, when it is graphed, it is a closed curve.
The Ellipse Has Two Foci
The ellipse is also a closed curve. If is formed when the plane that intersects the cone is tilted rather than perpendicular to the axis of the curve. The curve is the same distance from two foci, rather than from the center. When it is graphed, a line drawn through the segment formed by the fixed foci will be longer than a line drawn perpendicular to it.
The Parabola
The parabola is an open curve. It is formed when the plane that intersects the cone does not cut cleanly through the cone at the center, but cuts through it at an angle. It is the graph of a quadratic function. The axis of symmetry divides the parabola in half in such a way that both halves are mirror images of each other.
The Hyperbola
The hyperbola is also an open curve. It is formed when the plane that intersects the cone is parallel to a line from the long axis of the cone. The open curve then formed is a branch of the hyperbola. It has two foci that are outside the curve formed by the hyperbola.
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