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

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