If the equation has the term with y 2, then the axis of symmetry is along the x-axis and if the equation has the term with x 2, then the axis of symmetry is along the y-axis. Parabola is symmetric with respect to its axis.The following are the observations made from the standard form of equations: The transverse axis and the conjugate axis of each of these parabolas are different. The four standard forms are based on the axis and the orientation of the parabola. The below image presents the four standard equations and forms of the parabola. There are four standard equations of a parabola. 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 eccentricity of a parabola is equal to 1. It is the ratio of the distance of a point from the focus, to the distance of the point from the directrix. The endpoints of the latus rectum are (a, 2a), (a, -2a). The length of the latus rectum is taken as LL' = 4a. Latus Rectum: It is the focal chord that is perpendicular to the axis of the parabola and is passing through the focus of the parabola.The focal distance is also equal to the perpendicular distance of this point from the directrix. Focal Distance: The distance of a point \((x_1, y_1)\) on the parabola, from the focus, is the focal distance. The focal chord cuts the parabola at two distinct points.
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