Textbook of Engineering Drawing, Second Edition

4.38 Textbook of Enginnering Drawing-------------------

3. Through A and B draw lines parallel to CD. Through C and D draw lines parallel to AB and
   construct a parallelogram PQRS as shown in Fig. 4.55.


4. Repeat the procedure given in steps 4 to lOin above problem and complete the construction
   of the ellipse inside the parallelogram PQRS.

Problem : Construct a conic when the distance between its focus and its directrix is equal to
60 mm and its eccentricity is one. Name the curve. Draw a tangent at any point on the curve.

Solution : (Fig.4.56)

1. As the eccentricity of the conic is one, the curve is a parabola.


2. Draw the directrixDD and the axis AB perpendicular to DD. Mark the focus F such that

Fig. 4.55 Parallelogram Method

AF = 60 mm. By definition, VFNA = 1 and hence mark the point V, the vertex at the

midpoint of AF as shown in Fig.4.56.

3. Mark any number of points (say 6) on VB and draw verticals through these points.


4. With F as centre and Al as radius draw an arc to cut the vertical through point 1 at Pl'
   Similarly obtain points Pz' P 3 , P 4 , etc.


5. Draw a smooth curve passing through these points to obtain the required parabola.


6. Tangent at any point P on the parabola can be drawn as follows. From point P draw the
   ordinate PE. With V as centre and VE as radius draw a semicircle to cut the axis produced
   at G Join GP and extend it to T. Draw NP perpendicular to TP. Now, TPT and NPN are the
   required tangent and normal at P.
   Problem : A ball thrown from the ground level reaches a maximum height of 5 m and travels a
   horizontal distance of 12 m from the point of projection. Trace the path of the ball.
   Solution : (Fig.4.57)


7. The ball travels a horizontal distance of 12 m. By taking a scale of 1: 100, draw PS = 12 em
   to represent the double ordinate. Bisect PS at O.


8. The ball reaches a maximum height of 5 m. So from 0 erect vertical and mark the vertex V