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.

Answer Key

Solution

$(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$

$(x - 3)^2 + (y - 3)^2 + (z - 3)^2 = 3^2$

$(x^2 - 6x + 9) + (y^2 - 6y + 9) + (z^2 - 6z + 9) = 9$

$x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ ← answer

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