Equation of Sphere
The equation of a sphere in three-dimensional space with center coordinates (0, 0, 0) and radius “r” is:
x2 + y2 + z2 = r2
Here, (x, y, z) represents any point on the sphere’s surface. The equation signifies that the sum of the squares of the differences between the coordinates of any point on the sphere and the center point is equal to the square of the radius.
General Equation of Sphere
The general equation of a sphere in three-dimensional space is represented by the equation:
(x – h)2 + (y – k)2 + (z – l)2 = r2
Where (h, k, l) denotes the coordinates of the sphere’s center and r is its radius.
Parametric Equations of a Sphere
The parametric equations of a sphere in can be expressed as:
x = h + r × sin(θ) × cos(φ),
y = k + r × sin(θ) × sin(φ), and
z = l + r × cos(θ)
Where (θ, φ) are spherical coordinates representing the inclination angle and azimuth angle, respectively.
Read More about Parametric Equation.
Geometrical Interpretation of the Equation of a Sphere
The equation “(x – h)2 + (y – k)2 + (z – l)2 = r2” defines a sphere as the locus of points equidistant from its center (h, k, l). This implies that any point (x, y, z) on the sphere’s surface maintains a constant distance r from the center, illustrating the geometric property of a sphere.
Equation of a Sphere
The equation of a sphere defines all points equidistant from its center, given by (x – h)² + (y – k)² + (z – l)² = r², where (h, k, l) is the center and r is the radius. This article provides an in-depth exploration of the equation of a sphere, its properties, applications, and related concepts.
Table of Content
- What is Sphere?
- Equation of Sphere
- General Equation of Sphere
- Parametric Equations of a Sphere
- Geometrical Interpretation of the Equation of a Sphere
- Some other Equations of Sphere
- Surface Area Equation of Sphere
- Volume Equation of Sphere
- Derivation of Equation of Sphere
- Applications of the Equation of a Sphere
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