## 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.

Then,

This is the equation of the required sphere.

**Show that the equation ***x*^{2} + *y*^{2 }+ *z*^{2 }+ 2*ux* + 2*vy* + 2*wz* + *d* = 0 always represents a sphere. Find its centre ...