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.