Programmed tutorial: The Equation and Graph of a Sphere from a Point and Radius

We can identify h, k, l, and R from the data.

What do h, k, and l represent?

They describe the coordinates of the center of the sphere, (h, k, l)

What is the value of h here?

h = -2.

What is the value of k here?

k = 1.

What is the value of l here?

l = -3.

What does R represent?

R represents the radius of the sphere.

What is the value of R?

R = 4.

When we substitute the value of h,
do we get (x – 2) or (x – (-2) )?

We replace h by (-2) to get (x – (-2) ).

Combine these results to get the equation of this sphere.

The equation is

Simplify the equation.

Let’s plot this sphere, using the usual x-axis slanting out of the plane of the paper.

First plot the center of the sphere on paper and then click “Next” to check your diagram.

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Notice that the blue h-value is measured in the negative x-direction,
the yellow k-value is in the positive y-direction,
and the green l-value is measured downward (in the negative z-direction).

Add the outline of the sphere to your diagram and click “Next” to check.

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Add the “equator” of the sphere (the intersection of the sphere with a plane parallel to the x-y plane).

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Show the intersection with a plane parallel to the x-z plane (similar to the longitudinal arcs on a globe).

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The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor