# How do you find an equation of the sphere with center (2, -6, 4) and radius 5?

##### 1 Answer

Jun 16, 2016

The equation can be written in the form:

#(x-2)^2+(y-(-6))^2+(z-4)^2 = 5^2#

#### Explanation:

Given any two points

#d = sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

So for a sphere with centre

#5 = sqrt((x-2)^2+(y-(-6))^2+(z-4)^2)#

Squaring both sides and transposing this becomes:

#(x-2)^2+(y-(-6))^2+(z-4)^2 = 5^2#

This is in the form:

#(x-a)^2+(y-b)^2+(z-c)^2 = r^2#

with

Note the similarity with the equation of a circle with centre

#(x-h)^2+(y-k)^2 = r^2#