To write the equation of a sphere in standard form, you first need to understand what the equation entails. The standard form of the equation of a sphere is given by:
(x – h)² + (y – k)² + (z – l)² = r²
Here, (h, k, l) represents the coordinates of the center of the sphere, while r denotes the radius of the sphere.
Now, let’s break down the steps to formulate this equation:
- Identify the center of the sphere: Determine the coordinates of the center. Suppose the center is at point (h, k, l), where h, k, and l are the x, y, and z coordinates respectively.
- Find the radius: Measure the distance from the center of the sphere to any point on its surface. This distance is the radius r.
- Substitute values: Plug the coordinates of the center and the radius into the standard equation:
For example, if the center of your sphere is at (3, -2, 5) and the radius is 4, the equation would be:
(x – 3)² + (y + 2)² + (z – 5)² = 16
This equation reflects the geometric relationship that describes all points (x, y, z) in three-dimensional space that are a fixed distance (the radius) from the center of the sphere.
By following these steps, you can easily formulate the equation of any sphere in standard form!