Equation of a Sphere with Center (h,k,l) and radius r
The equation of a sphere with center (h, k, l) and radius r can be derived using the distance formula in three-dimensional space
The equation of a sphere with center (h, k, l) and radius r can be derived using the distance formula in three-dimensional space. The distance between any point (x, y, z) on the sphere and the center (h, k, l) should be equal to the radius r.
The distance formula in three-dimensional space is given by:
d = √((x – h)^2 + (y – k)^2 + (z – l)^2)
We want this distance to be equal to the radius r. Therefore, we can set up the equation:
√((x – h)^2 + (y – k)^2 + (z – l)^2) = r
To simplify the equation, we can square both sides:
((x – h)^2 + (y – k)^2 + (z – l)^2) = r^2
Expanding the terms within the parentheses:
(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2
This is the general equation of a sphere with center (h, k, l) and radius r.
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