Construction of Parabola
Sample Problem 1:
a)Construct a Parabola when the distance focus and the directrix is 40mm. Draw tangent and normal at any point r on your curve.
Steps to Construction of Parabola:
- Draw directrix DD. At any point C on it draw axis CA ⊥r to DD.
- Distance between the focus and the directrix is 40mm. So mark F the focus, such that CF=40mm.
- For parabola, e is 1; so construct the right angled ΔCXY such that XY/CX = 1 (X is any point on axis).
- From F draw a 45º line to intersect CY at s.
- From S erect vertical to cut CF at vertex V.Now SV = FV.
- From similar Δs Cthe points 1,2,…,5 at approximately equal interXY and CVS, SV/CV = XY/CX = FV/CV = 1.
- Along the axis CA mark the points 1,2,…,5 at approximately equal intervals.
- Through 1,2,..,5 erect verticals to intersect the line CY (produced if necessary) at 1′,2′,…,5′ respectively.
- With 11′ as radius and F as center, Draw two arcs on either side of the axis to intersect the vertical line drawn through 1 at P1 and P1′.
- Repeat the above and obtain P2 & P2′,P3 & P3′,….,P5&P5′ corresponding to points 2,3,4,5 respectively. Draw a smooth parabola through P5,…,P1,V,P1′,etc.
- Tangent and Normal: Join PF. At F, draw a perpendicular to QP. NM is the normal.
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