Procedure

1. To draw a parabola with a given distance of focus from the directrix. Also, draw a normal and a tangent at a given point from the directrix.

1. Draw the axis AB and directrix CD perpendicular to each other.
2. Mark the point as focus F at a distance given from the directrix.
3. Mark the vertex V on the axis such that VF= AV.
4. From V, draw a perpendicular line VE whose length is equal to VF.
5. Join VE with point A and produce the line such that the eccentricity is equal to 1.
6. Mark points 1, 2,3, 4, 5 and so on to the right-hand side of V.
7. Through each of the points, raise perpendicular lines meeting AE at points 1’,2’, 3’,4’, 5’ and so on.
8. Take a radius of 1-1’ and with F as the centre, draw arcs on the line for the first point on either side of the axis. Mark the points as P1 and P1’ respectively.
9. Repeat the same procedure for the rest of the points.
10. Join all the points obtained by marking off arcs. The smooth curve so obtained is the required parabola.
11. Locate the point in the parabola where the tangent and normal has to be drawn.
12. Join the point with the focus. Draw a line perpendicular to it such that it's one end touches the directrix. Mark it as T.
13. From T, draw a line passing through the desired point and extend it. This is the required Tangent.
14. Draw a line on the desired point that is perpendicular to the tangent. This is the required normal.

2. To draw an ellipse with a given distance of focus from the directrix having an eccentricity equal to 2/3. Also, draw a tangent and normal at a given point from the directrix.

1. Draw the axis AB and directrix CD perpendicular to each other.
2. Mark the point as focus F at a distance given from the directrix.
3. Divide AF into five equal segments.
4. Locate the vertex V from the third division from point A or from second division from point F. So the eccentricity e= 2/3.
5. From the vertex draw a perpendicular line VE that is equal to VF. Join AE and extend it.
6. Mark points 1, 2,3, 4, 5 and so on to the right-hand side of V.
7. Through each of the points, raise perpendicular lines meeting AE at points 1’,2’, 3’,4’, 5’ and so on.
8. With a radius of 1-1’ and having F as the centre, mark arcs on the line for the first point on either side of the axis. Mark the points as P1 and P1’ respectively.
9. Correspondingly, locate the points P2, P2’, P3, P3’ and so on.
10. A closed curve is formed by joining all the points which is the required ellipse. It has two directories and two foci.
11. Mark the point in the ellipse where the tangent has to be constructed.
12. Join the point with the focus and draw a line perpendicular to it. Name its one end as T.
13. Draw a line from T, passing through the point and extend it. This is the required tangent.
14. Draw a line perpendicular to the tangent on the desired point. This is the required normal.

3. To draw a hyperbola at a given distance of focus from the directrix having an eccentricity equal to 3/2. Also, draw a normal and a tangent at a given point from the directrix.

1. Draw the axis AB and directrix CD perpendicular to each other.
2. Mark the point as focus F at a distance given from the directrix.
3. Divide AF into 5 equal parts.
4. Mark the vertex V on the point from the third division of focus. Draw a perpendicular line VE whose length is equal to VF.
5. Join AE and produce the line.
6. From V locate points 1, 2, 3 and so on, on the axis.
7. Draw perpendicular lines from each of the points meeting the line AE at points 1’,2’, 3’ and so on.
8. Take 1-1’ as the radius and have F as the centre draw arcs on each of the lines on either side of the axis.
9. Obtain the points P1, P1’, P2, P2, and so on.
10. Join all the points and curve so obtained is a hyperbola.