7.5.1 Introduction: A parabola is the locus of all points in a plane equidistant from a fixed point, called the focus, and a fixed straight line, called the directrix.
In the parabola shown in figure 2-8, point V, which lies halfway between the focus and the directrix, is called the vertex of the parabola. In this figure and in many of the parabolas discussed in the first portion of this section, the vertex of the parabola falls at the origin; however, the vertex of the parabola, like the center of the circle, can fall at any point in the plane.
7.5.2 Standard equation of Parabola:
Take a point F(a, 0) as the focus, where a> 0.
A line D with equation x = -a is taken as directrix.
Let P(x, y) be a point on locus and PM is the perpendicular on the directrix.
PF = PM
PF2 = PM2
(x – a )2 + y2 = (x + a)2
y2 = (x + a)2 – (x – a)2
y2 = 4ax
this is the standard equation of parabola.
Focus = F(a, 0)
Vertex = O(0, 0)
Equation of axis; y = 0
Equation of directrix; x + a = 0
To Schedule a Parabola tutoring session
To submit Parabola assignment click here.
Geometry Help | Calculus Help | Math Tutors | Algebra Tutor | Tutorial Algebra | Algebra Learn | Math Tutorial | Algebra Tutoring | Calculus Tutor | Precalculus Help | Geometry Tutor | Maths Tutor | Geometry Homework Help | Homework Tutor | Mathematics Tutor | Calculus Tutoring | Online Algebra Tutor | Geometry Tutoring | Online Algebra Tutoring | Algebra Tutors | Math Homework Helper | Calculus Homework Help | Online Tutoring | Calculus Tutors | Homework Tutoring
Assignment Writing Help
Engineering Assignment Services
Do My Assignment Help
Write My Essay Services