Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so that the coefficient of x2 is 1.

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(Expand to obtain an equivalent expression for the sphere: )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

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Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

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In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between and would be:

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In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

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The equation for a sphere of radius and center would be:

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In this case, the equation would be:

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Simplify to obtain:

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Expand the squares and simplify to obtain:

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just keep asking questions until you have a better understanding.

step-by-step explanation: