Summary:
1. What is Parabola?
2. Use of Parabola.
3. Methods of construction of a Parabola.
4. How to draw Tangent and Normal on a Parabola?
What is a Parabola or Parabolic Curve?
When a curve is generated by cutting out a conic in such a way that the section plane is parallel to one of its generators of the conic, it is called a Parabola or Parabolic Curve.
Use of Parabola or Parabolic Curves
Practically, in engineering drawing, the Parabolic curves are used to draw arches, bridges, sound reflectors, light reflectors, etc. Thus, it has a huge application in architectural drawing and civil engineering drawing.
Methods of construction of a Parabola
(1) Eccentricity Method or General Method or Common Method
It’s similar to drawing an ellipse in the Eccentricity method. Taking that same assumption into account! Draw a Parabola, where the distance between the directrix to focus is 50 mm.
As we know, the eccentricity of the Parabola is equal to 1.
(i) First of all, draw the directrix AB and the axis CD as shown in Fig.
(ii) Mark focus point F on axis CD, 50 mm apart from C.
(iii) Now, bisect CF to get the vertex point V (because
eccentricity = 1,
therefore, VF=CV). Mark point E on the bisector such as VE=VF.
(iv) Draw
a straight line joining C and E, and extend this line to a convenient length.
.webp "Parabola drawn by Eccentricity Method")
(v) From point V, mark a number of points 1, 2, 3, etc. on the axis, and through them, draw perpendiculars to intersect CE at 1', 2', 3', etc respectively. See image.
(vi) Now, take the center as point F and a radius equal to 1-1', and draw arcs to intersect the perpendicular through 1 on both sides of the axis at points P1 and P'1.
(vii) Similarly, take the center as F on the axis and obtain points P2 and P'2, P3 and P'3.
(viii) Now, with the help of French curves draw a smooth and thick curve to get the required parabola through these points.
For Parabola only, you can follow these steps too as described below for drawing a Parabola in the Eccentricity method (2nd Kind) more easily!
(i) First of all, draw the directrix AB and the axis CD as shown in Fig.
(ii) Mark focus point F on axis CD, 50 mm apart from C.
(iii) Now, bisect CF to get the vertex point V (because
eccentricity = 1, therefore,
VF=CV).
(iv) From point V, mark a number of points 1, 2, 3, etc. on the axis, and through them, draw perpendiculars to it. See image.
.webp "Parabola drawn by Eccentricity Method")
(v) Now, take the center as F and radius equal to C1, and draw arcs cutting the perpendicular through 1 on both sides of the axis at P1 and P'1.
(vi) Similarly, locate points P2 and P'2,
P3 and P'3, P4 and P'4
on both the sides of the axis.
(vii) Draw a smooth and thick curve through these points with the help of French curves to get that required Parabola.
2. Draw a Parabola in Rectangle Method
(ii) At its mid-point E,
draw the axis EF perpendicular
(90˚) to AB.
(iii) Construct
a rectangle ABCD, making side
DC equal to AB and side AD = BC =
EF.
(iv) Now, divide lines AD and AE into the same number of equal parts (Say 4) and name them as
Shown in the image (starting from A).
(v) Similarly, divide lines BC and BE into the same number of equal parts (Say 4) and name them as
Shown in the image (starting from B).
(v) Now, join F with points 1, 2, 3, 4, 5, and 6 in straight lines.
(vi) Draw perpendiculars through 1 ', 2', 3', 4', 5', and 6' to intersect F1, F2, F3, F4, F5, and F6 at points P1, P2, P3, P4, P5, and P6 respectively.
(vi) Now, join points A, P1, P2, P3, P4, P5, P6, and B with a smooth thick curve to get the required Parabola by Rectangle Method.
3. Draw a Parabola in the Parallelogram Method
(This method is similar to the Rectangle Method, except we construct a Parallelogram to draw the required Parabola here.)
(i) Draw the baseline AB and find its midpoint E.
(ii) At its mid-point E,
draw the axis EF at
ɵ˚ to AB.
(iii) Construct
a parallelogram ABCD, making
side DC parallel to AB, and side AD and BC
parallel to EF.
(iv) Now, divide lines AD and AE into the same number of equal parts (Say 6) and name them as
Shown in the image (starting from A).
(v) Similarly, divide lines BC and BE into the same number of equal parts (Say 6) and name them as
Shown in the image (starting from B).
(v) Now, join F with points 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 by straight lines.
(vi) Draw perpendiculars through 1 ', 2', 3', 4', 5', 6', 7', 8', 9', and 10' to intersect F1, F2, F3, F4, F5, F6, F7, F8, F9, and F10 at points P1, P2, P3, P4, P5, P6, P7, P8, P9, and P10 respectively.
(vii) Now, join points A, P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, and B with a smooth-thick curve to get the required Parabola by Parallelogram Method.
4. Draw a Parabola by Tangent Method
(i) Draw the baseline AB and find the middle point on it to draw the axis EV.
(ii) Extend EV
up to F so that EV = VF ( as Eccentricity in Parabola is equal to
1 and here, F is the Vertex point).
(iii) Join point F with A and B with straight
lines so that OA = OB (Most important factor to draw a Parabola by Tangent
Method).
(iv) Now, divide lines FA and FB into the same number of equal parts, say 8.
(v) Name the division points as shown in the image.
(vi) Now, join 1 with 1 ', 2 with 2', 3 with 3', 4 with 4', 5 with 5', 6 with 6', and 7 with 7' by straight lines which will be the tangents of the parabola.
(vii) At last, draw a smooth and thick curve starting from point A and tangent 1-1', 2-2', 3-3', 4-4', 5-5 , 6-6', 7-7', and point B to get the required parabola.
How to draw Tangent and Normal on a Parabola
Drawing a Tangent and Normal on a Parabola, Hyperbola, or Ellipse is quite similar. However, you can learn it from the topic Ellipse too yet I'm providing that here again.
(i) Assume a point P through which we’ll draw a Tangent and Normal on the Parabola.
(ii) Now, join the focus point F with the point P by a straight line.
(iii) Take the FP line as the base, and draw a right angle (90˚) at point F, in such a way that line FT will intersect the directrix (AB) at point T.
(iv) Join T and P by a straight line to get the Tangent of the parabola at point P.
(v) Now, take the TP line as the base, and draw a right angle (90˚) at point P.
(vi) So, the NPM is the required Normal of the Parabola on that point P.