Page 73 - Mathematics Class - XI

2. When the transparent plane sheet cuts the second cone in such a way that the sheet is inclined slightly to
the axis of the cone. The section, so obtained, is an ellipse.

Fig. (c)

3. When the transparent plane sheet cuts the third cone in such a way that the sheet is parallel to the slant
height of the cone. The section, so obtained, is a parabola and it is shown in fig. (d).
4. When the transparent plane sheet cuts the fourth cone in such a way that the plane sheet is parallel to the
axis of the cone. The sections, so obtained, is a part of a hyperbola and it is shown in fig (e).

Fig. (d) Fig. (e)

OBSERVATION
1. In Fig. (b), the transparent sheet is parallel to the base of the cone. The conic section, so obtained, is circle.

2. In Fig. (c), the transparent sheet is inclined to the axis of the cone. The conic section, so obtained, is an
ellipse.

3. In Fig. (d), the transparent sheet is parallel to the slant height of the cone. The conic section, so obtained,
is parabola.

4. In Fig. (e), the transparent plane sheet is parallel to the axis of the cone. The conic section, so obtained,
is a part of hyperbola.

CONCLUSION
This activity shows that the various types of conic sections like, circle, ellipse, parabola, hyperbola can be
constructed.

APPLICATION
This activity helps in understanding various types of conic sections and their applications in real life.

Knowledge Booster
The equation of a circle comes in two forms:
● The standard form: (x – h) + (y – k) = r 2
2
2
● The general form: x + y + 2gx + 2fy + c = 0
2
2
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