Find the equation of a sphere, whose centre is (1,1,1) and radius is 5 units
Sphere can be thought of as a three dimensional extension of a circle. Similar to distance formula and section formula, the equation of sphere has additional terms involving z coordinate. To find the equation of the sphere, let’s consider a general point P(x,y,z) on the sphere. Let the centre of the sphere be O(1,1,1). We are given that the radius is 5 units.
Distance of P from O will be equal to the radius, that is 5 units. Using distance formula, we get
This is the equation of the sphere with centre (1,1,1) and radius 5 units