1. Mathematics

2. Three Dimensional Geometry–3(Sphere)
Session
Three Dimensional Geometry–3(Sphere)

3. Session Objectives Equation of a Sphere; Vector Form, Cartesian Form
General Equation of a Sphere
Diameter Form; Vector Form, Cartesian Form
Section of a Sphere by a Plane
Class Exercise

4. Sphere
A sphere is the locus of a point in space, which moves in such a way
that its distance (called radius) from a fixed point (called centre)
remains constant.

5. Equation of a Sphere (Vector Form)

6. Cartesian Form

7. Characteristics

8. General Equation of a Sphere

9. Example –1

10. Example –2

11. Solution Cont.

12. Example -3
(i) passes through (0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c)

13. Solution Cont.

14. Diameter Form (Vector Form)

15. Cartesian Form

16. Example –4

17. Solution Cont.

18. Example –5

19. Solution Cont.

20. Section of a Sphere by a PlaneM
Let C be the centre of the sphere and M be the foot of the perpendicular
from C on the plane. Then M is the centre of the circle and radius of the
circle is given by

21. A Plane Touches a Given Sphere
The perpendicular distance from the centre of the sphere to the plane
= the radius of the sphere

22. Example –6 O A B M

23. Example –7

24. Solution Cont.

25. Thank you