Table of Contents

- 1 How do you find the equation of a sphere when given two points?
- 2 What is the general equation of sphere?
- 3 What is the volume equation for a sphere?
- 4 What is the equation of the YZ plane?
- 5 What is the difference between a 0-sphere and a 2-sphere?
- 6 How do you find the equation of an imaginary sphere?

## How do you find the equation of a sphere when given two points?

The general equation of a sphere is: (x – a)² + (y – b)² + (z – c)² = r², where (a, b, c) represents the center of the sphere, r represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.

## What is the general equation of sphere?

The general equation of the sphere is x2 + y2 + z2 = r2 and in this article, we will learn about deriving the equation of a sphere along with its volume and surface area.

**What is the intersection of this sphere with the YZ plane?**

The intersection of this sphere with the yz-plane is the set of points on the sphere whose x-coordinate is 0. Putting x = 0 into the equation, we have 9 + (y – 2)2 + (z – 5)2 = 16, x = 0 or (y – 2)+ (z – 5)2 = 7, x = 0, which represents a circle in the yz-plane with center (0, 2, 5) and radius V7.

### What is the volume equation for a sphere?

The formula for the volume of a sphere is V = 4/3 πr³. See the formula used in an example where we are given the diameter of the sphere.

### What is the equation of the YZ plane?

∵ x coordinate gives the distance of a point from yz plane. ∴ x = 0 implies that the point lies on yz plane. Thus, locus of a point for which x = 0 is the yz plane or we can say that equation of yz plane is x = 0.

**How to find center and radius from the equation of the sphere?**

How to find the center and radius from the equation of the sphere. Example. Find the center and radius of the sphere. x 2 + 2 x + y 2 − 2 y + z 2 − 6 z = 1 4 x^2+2x+y^2-2y+z^2-6z=14 x 2 + 2 x + y 2 − 2 y + z 2 − 6 z = 1 4. We know we eventually need to change the equation into the standard form of the equation of a sphere,

#### What is the difference between a 0-sphere and a 2-sphere?

In particular: S 0: a 0-sphere is a pair of endpoints of an interval [−r, r] of the real line S 1: a 1-sphere is a circle of radius r S 2: a 2-sphere is an ordinary sphere S 3: a 3-sphere is a sphere in 4-dimensional Euclidean space.

#### How do you find the equation of an imaginary sphere?

In analytic geometry, a sphere with center (x 0, y 0, z 0) and radius r is the locus of all points (x, y, z) such that. Let a, b, c, d, e be real numbers with a ≠ 0 and put. Then the equation. has no real points as solutions if ρ < 0 {displaystyle rho <0} and is called the equation of an imaginary sphere.

**What is the volume of a sphere in three dimensions?**

In three dimensions, the volume inside a sphere (that is, the volume of a ball, but classically referred to as the volume of a sphere) is. where r is the radius and d is the diameter of the sphere.