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Parabola: The locus of a point which moves such that its distance from vertex 0 0 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.

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.

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Katherine Johnson is the pioneering NASA mathematician who was integral to the successful and safe flight and return of many human missions as well as satellites. Prior to the work featured in the movie Hidden Figures , she had already made major contributions to the space program. She provided trajectory analysis for the Mercury mission, in which Alan Shepard became the first American to reach space, and she and engineer Ted Sopinski authored a monumental paper regarding placing an object in a precise orbital position and having it return safely to Earth. Many of the orbits she determined were made up of parabolas, and her ability to combine different types of math enabled an unprecedented level of precision.

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TS TET. JSSC Constable. RBI Assistant. AP TET. Rajasthan Pre D. 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. SBI Clerk. KSP Constable. Chandigarh Police ASI. MBA Entrance Exam. Bihar Upper Primary Teacher. Since the vertex is at 0, 0 and the focus is at 0, 4 which lies on the y-axis, the y-axis is the axis of the parabola. Odisha Assistant Agriculture Officer. It follows that:.