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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. 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.

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This is the vertex form calculator also known as vertex calculator or even find the vertex calculator. If you want to know how to find the vertex of a parabola , this is the right place to begin. Moreover, our tool teaches you what the vertex form of a quadratic equation is and how to derive the equation of the vertex form or the vertex equation itself. And this is not the end! This calculator also helps you convert from the standard to the vertex form of a parabola, or even the other way round , in a blink of an eye! Try our parabola calculator! The vertex of a parabola is a point that represents the extremal value of a quadratic curve. The quadratic part stands because the most significant power of our variable x is two. The vertex can be either a minimum for a parabola opening up or a maximum for a parabola opening down. Alternatively, we can say that the vertex is the intersection of the parabola and its symmetry axis.

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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.

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Notice that the axis of symmetry passes through the focus and vertex and is perpendicular to the directrix. NCL Staff Nurse. CAT Exam. Bihar Police Constable. Telangana High Court Field Assistant. AP Animal Husbandry Assistant. If the plane is parallel to the edge of the cone, an unbounded curve is formed. Improve this page Learn More. WB Police. Sanitary and Waste Mgmt. Bhulekh Maharashtra. West Bengal Judicial Service. CG Vyapam Assistant Grade 3.