Mathematics

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

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

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.

Equation of a Sphere (Vector Form)

Cartesian Form

Characteristics

General Equation of a Sphere

Example –1

Example –2

Solution Cont.

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

Solution Cont.

Diameter Form (Vector Form)

Cartesian Form

Example –4

Solution Cont.

Example –5

Solution Cont.

Section of a Sphere by a Plane M 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

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

Example –6 O A B M

Example –7

Solution Cont.

Thank you