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The given equation is in xy - plane. It is a Parabola with horizontal axis of symmetry and vertex in the origin. Each and every point of the parabola must satisfy this relation. Also, parametric equations represent each point of the parabola as a function of parameter 't'. Last updated on Mar 31,

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A parabola is a graph of a quadratic function. Pascal stated that a parabola is a projection of a circle. Galileo explained that projectiles falling under the effect of uniform gravity follow a path called a parabolic path. Many physical motions of bodies follow a curvilinear path which is in the shape of a parabola. In mathematics, any plane curve which is mirror-symmetrical and usually of approximately U shape is called a parabola. Here we shall aim at understanding the derivation of the standard formula of a parabola, the different equations of a parabola, and the properties of a parabola. A parabola refers to an equation of a curve, such that each point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the "focus" of the parabola, and the fixed line is called the "directrix" of the parabola. Also, an important point to note is that the fixed point does not lie on the fixed line. Thus, a parabola is mathematically defined as follows:. Parabola is an important curve of the conic sections of the coordinate geometry. Here are the formulas to find the equation of the axis, directrix, vertex, focus, and length of the latus rectum of different types of parabolas. The four standard forms are based on the axis and the orientation of the parabola. The transverse axis and the conjugate axis of each of these parabolas are different. The following are the observations made from the standard form of equations:.

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A parabola is a graph of a quadratic function. Pascal stated that a parabola is a projection of a circle. Galileo explained that projectiles falling under the effect of uniform gravity follow a path called a parabolic path. Many physical motions of bodies follow a curvilinear path which is in the shape of a parabola. In mathematics, any plane curve which is mirror-symmetrical and usually of approximately U shape is called a parabola. Here we shall aim at understanding the derivation of the standard formula of a parabola, the different equations of a parabola, and the properties of a parabola. A parabola refers to an equation of a curve, such that each point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the "focus" of the parabola, and the fixed line is called the "directrix" of the parabola.

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In conic sections , a parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point not on the line in the plane. A line through the focus and perpendicular to the directrix is called the axis of the parabola. Also, the vertex is the point of intersection of a parabola with the axis. As we know, the standard equation of the parabola is used in solving a variety of problems in maths. In this article, you will learn how to write the standard equations for parabola in different cases and how to solve questions based on these equations. In this section, one can learn what is the standard equation of a parabola and how to write the equations of parabola. The parabola equation is simplest if the vertex is at the origin and the axis of symmetry is along the x-axis and y-axis. The four such possible orientations of the parabola are explained in the table below:. These four equations are called standard equations of parabolas. It is important to note that the standard equations of parabolas focus on one of the coordinate axes, the vertex at the origin.

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A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point known as the focus and from a fixed straight line, which is known as the directrix. Parabola is an integral part of the conic section topic, and all its concepts are covered here.

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