Equation of the sphere of radius 3 and tangent to coordinate-planes Date of Exam May 2016 Subject Mathematics, Surveying and Transportation Engineering Problem Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant. A. $x^2 + y^2 + z^2 - 9 = 0$ B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ Answer Key Click here to show or hide the answer key [ B ] Solution Click here to expand or collapse this section Center (h, k, l) is at C(3, 3, 3) Radius, r = 3 $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$ $(x - 3)^2 + (y - 3)^2 + (z - 3)^2 = 3^2$ $(x^2 - 6x + 9) + (y^2 - 6y + 9) + (z^2 - 6z + 9) = 9$ $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ ← answer Category Analytic Geometry Rectangular Coordinates Space Coordinates Sphere Equation of Sphere Log in to post comments
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