A parabola is a curve traced by a point, moving such that, at any position ,its distance from the fixed point (focus) is always equal to its distance from a fixed straight line (directrix)
parabola can be constructed in many ways.. like eccentricity method, triangle method, oblong or rectangle method etc....
triangle method of construction is based on tangents..
- Draw the base AB and axis CD , such that CD is perpendicular bisector to AB.
- produce CD to E such that DE = CD.
- join E,A and E, B. these are the tangents to the parabola at A and B.
- Divide AE and BE in to the same number of the equal parts and number the points as shown.
- join 1,1' ; 2,2' ; 3,3'; etc.... forming the tangents to the required parabola
- A smooth curve passing through A,D and B tangential to the above lines is the required parabola
hence the required parabola through triangle method