Find an equation of the sphere that passes through the point (5, 6, −2) and has center (2, 7, 4). Step 1 Recall that the equation of a sphere with radius r and center (a, b, c) is given by (x − a)2 + y − ? a b c r 2 + z − ? a b c r 2 = ? a b c r 2.
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Find an equation of the sphere determined by the given information: passes through the point (5, 6, -4), center (2, 7, 2) 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 If the sphere passes through (5, 6, -4) and has center (2, 7, 2), then its radius is the distance between these two points. Therefore, r = √((2 - 5)^2 + (7 - 6)^2 + (2 - )^2) = √(9 + 1 + ) = √( ).
Adi S.
Find an equation of the sphere that passes through the point (7, 4, -6) and has center (4, 7, 6). 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. 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). 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.
Zhumagali S.
Find an equation of the sphere that passes through the point (6, -5, 3) and has center at (-3, 5, 3).
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