Question

Find an equation of the sphere that passes through the point (7, 4, -6) and has center (4, 7, 6). Part 1 of 3 Recall that the equation of a sphere with radius $r$ and center ($a$, $b$, $c$) is given by $(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2$. Part 2 of 3 If the sphere passes through (7, 4, -6) and has center (4, 7, 6), then its radius is the distance between these two points. Therefore, $r = sqrt{(4 - 7)^2 + (7 - 4)^2 + (6 - (-6))^2}$ $= sqrt{9 + 9 + 144}$ $= sqrt{162}$. Part 3 of 3 Substituting this radius and the given center into the equation of a sphere, we therefore conclude that the equation of the given sphere is as follows.

          Find an equation of the sphere that passes through the point (7, 4, -6) and has center (4, 7, 6).
Part 1 of 3
Recall that the equation of a sphere with radius $r$ and center ($a$, $b$, $c$) is given by
$(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2$.
Part 2 of 3
If the sphere passes through (7, 4, -6) and has center (4, 7, 6), then its radius is the distance between
these two points.
Therefore,
$r = sqrt{(4 - 7)^2 + (7 - 4)^2 + (6 - (-6))^2}$
$= sqrt{9 + 9 + 144}$
$= sqrt{162}$.
Part 3 of 3
Substituting this radius and the given center into the equation of a sphere, we therefore conclude that the
equation of the given sphere is as follows.

Find an equation of the sphere that passes through the point (7, 4, -6) and has center (4, 7, 6).
Part 1 of 3
Recall that the equation of a sphere with radius r and center (a, b, c) is given by
(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2.
Part 2 of 3
If the sphere passes through (7, 4, -6) and has center (4, 7, 6), then its radius is the distance between
these two points.
Therefore,
r = sqrt(4 - 7)^2 + (7 - 4)^2 + (6 - (-6))^2
= sqrt9 + 9 + 144
= sqrt162.
Part 3 of 3
Substituting this radius and the given center into the equation of a sphere, we therefore conclude that the
equation of the given sphere is as follows.

Added by Samantha T.

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