Page 76 - Mathematics Class - XI

8. Take some more points B , B , ... on the line m and repeat the above process to obtain points P , P , ...,
3
3
4
4
respectively.
9. Draw a free hand curve through the points P , P , P , P , ... (Fig. (a)).
2
1
3
4
DEMONSTRATION
The points P , P , P , P , ... are such that the distance of each point from the fixed point A is same as the distance
3
1
2
4
of the point from the line m.
OBSERVATION
1. P B = ___________ and P A = ___________
1 1 1
2. P B = ___________ and P A = ___________
2
2
2
3. P B = ___________ and P A = ___________
3
3
3
4. P B = ___________ and P A = ___________
4 4 4
5. P B = ___________ and P A = ___________
5 5 5
6. We observe that distances of the points P , P , P , P ... from the points B , B , B , B ... are same as to the
3
1
2
1
4
4
2
3
distances of these points from the fixed point A.
7. Therefore, the free hand curve obtained by joining P , P , P , ... is a parabola with directrix m and focus A.
1
2
3
CONCLUSION
This activity shows that any point on parabola is equidistant from focus and directrix.
APPLICATION
This activity is useful in understanding the terms related to parabola like focus, directrix, property of the point
on the parabola.

Knowledge Booster
● Latus rectum of a parabola is a line segment
perpendicular to the axis of the parabola,
through the focus and whose end points lie
on the parabola.
● Length of the latus rectum of the parabola
y = 4ax is 4a.
2

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