Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

The standard equation of the sphere is

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint =

Let the first endpoint be represented as and the second endpoint be .

Hence,

Midpoint =

Midpoint =

Midpoint =

Midpoint =

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

This is the diameter

To find the radius, r

From

∴

r =

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is

Radius of the sphere is

The equation of a sphere of radius r and center is given by

Hence, the equation of the sphere of radius and center is

This is the standard equation of the sphere

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