To write the equation of a sphere in standard form, you need to know the center of the sphere and its radius. The standard form of a sphere’s equation is given by:
(x – h)² + (y – k)² + (z – l)² = r²
In this equation, (h, k, l) represents the coordinates of the center of the sphere, and r is the radius.
For example, if you have a sphere with a center at the point (2, -3, 5) and a radius of 4, you would substitute these values into the standard form:
(x – 2)² + (y + 3)² + (z – 5)² = 4²
This simplifies to:
(x – 2)² + (y + 3)² + (z – 5)² = 16
Thus, the equation of the sphere in standard form is ready to use! Remember, identifying the center and radius is key to forming the correct equation.