About Parabola Formula
Parabola refers to the graph of a quadratic function. A circular projection, according to Pascal. According to Galileo, projectiles falling under the influence of uniform gravity follow a parabolic path. Many physical motions follow a curved path in the shape of a parabola. In mathematics, a parabola is a mirror-symmetrical planar curve with a U-shape.
What do you mean by Parabola?
A parabola is an equation for a curve in which a point on the curve is equidistant from both a fixed point and a fixed-line. The focus of the parabola is the fixed point, and the directrix of the parabola is the fixed line. It should also be noted that the fixed point is not on the fixed line. A parabola is a point that is equidistant from a given point (focus) and a specific line (directrix). The parabola is an important curve in the conic sections of coordinate geometry. Parabola Equation
Parabola's general equation is y = a(x-h)2 + k or x = a(y-k)2 +h, Here (h,k) is the vertex. A normal parabola's standard equation is y2 = 4ax.
The terminology listed below will help you comprehend the characteristics and elements of a parabola.
Focus: The focus of the parabola is the point (a, 0).
Directrix: The parabola's directrix is a line drawn parallel to the y-axis and passing through the point (-a, 0). The parabola's axis is perpendicular to the directrix.
Focal Chord: Focal chord of a parabola is the chord that passes through the parabola's focus. The parabola is cut in two places by the focal chord.
Focal Distance: Focal distance is the distance between a point (x1,y1)(x1,y1) on the parabola and the focus. The perpendicular distance of this point from the directrix is also equal to the focal distance.
Latus Rectum: It is the focal chord, which is perpendicular to the parabola's axis and passes through the parabola's focus. LL' = 4a represents length of latus rectum. (a, 2a) are the latus rectum's ends (a, -2a).
Eccentricity: (e = 1). It's the proportion of a point's distance from the focus to its distance from the directrix. A parabola's eccentricity is equal to 1.
Parabola Formula
Parabola Formula helps in representing the general form of the parabolic path in the plane. The following are formulas that are used to get the parameters of a parabola.
The direction of the parabola is determined by the value of a.
- Vertex is (h,k), where h is equal to -b/2a and k = f(h)
- Latus Rectum is 4a
- Focus: (h, k+ (1/4a))
- Directrix: y = k - 1/4a
Download all the Maths formulas from the HT maths page.
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