Vertex 0 0

Parabola: The locus of a point which moves such that its distance from a fixed point is equal to its distance from a fixed straight line.

In The Ellipse we saw that an ellipse is formed when a plane cuts through a right circular cone. If the plane is parallel to the edge of the cone, an unbounded curve is formed. This curve is a parabola. Like the ellipse and hyperbola , the parabola can also be defined by a set of points in the coordinate plane. Now we extend the discussion to include other key features of the parabola.

Vertex 0 0

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To our surprise and delight, we may also define parabolas in terms of distance. The vertex is the point on the parabola closest to the focus. We want to use only the distance definition of parabola to derive the equation of a parabola and, if all is right with the universe, we should get an expression much like those studied in Section 2. Our picture becomes. Using the Distance Formula, Equation 1. This is a quick way to distinguish an equation of a parabola from that of a circle because in the equation of a circle, both variables are squared. We recognize this as the form given in Equation 7. Of all of the information requested in the previous example, only the vertex is part of the graph of the parabola.

Vertex 0 0

In The Ellipse we saw that an ellipse is formed when a plane cuts through a right circular cone. If the plane is parallel to the edge of the cone, an unbounded curve is formed. This curve is a parabola. Like the ellipse and hyperbola , the parabola can also be defined by a set of points in the coordinate plane. Now we extend the discussion to include other key features of the parabola. Notice that the axis of symmetry passes through the focus and vertex and is perpendicular to the directrix. The vertex is the midpoint between the directrix and the focus. The line segment that passes through the focus and is parallel to the directrix is called the latus rectum, also called the focal diameter. The endpoints of the focal diameter lie on the curve. To work with parabolas in the coordinate plane , we consider two cases: those with a vertex at the origin and those with a vertex at a point other than the origin.

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Any time you come across a quadratic formula you want to analyze, you'll find this parabola calculator to be the perfect tool for you.

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