Chapter 14

Sphere

14.1  DEFINITION OF SPHERE

The locus of a moving point in space such that its distance from a fixed point is constant is called a sphere. The fixed point is called the centre of the sphere. The constant distance is called the radius.

14.2  THE EQUATION OF A SPHERE WITH CENTRE AT (a, b, c) AND RADIUS R

Let P(x, y, z) be any point on the sphere. Let C(a, b, c) be the centre.

Equation

Then,

Equation

This is the equation of the required sphere.

Show that the equation x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 always represents a sphere. Find its centre ...

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