Asked by Sarah
A sphere consists of all the points that are 5 units from its center
(2, 3,−6). Write an equation that describes this sphere. Does the sphere intersect the xy-plane? Explain.
(2, 3,−6). Write an equation that describes this sphere. Does the sphere intersect the xy-plane? Explain.
Answers
Answered by
drwls
(x-2)^2 + (y-3)^2 + (z+6)^2 = 25
is the equation. That is the general equation for a sphere with the center coordinates and radius prescribed.
That should be obvious.
If it intersected the xy plane, there would be a solution for z = 0. That would require that
(x-2)^2 + (y-3)^2 + 36 = 25
which is impossible for real x and y.
You would be have a sphere of radius 5 with its center 6 units below the plane.
is the equation. That is the general equation for a sphere with the center coordinates and radius prescribed.
That should be obvious.
If it intersected the xy plane, there would be a solution for z = 0. That would require that
(x-2)^2 + (y-3)^2 + 36 = 25
which is impossible for real x and y.
You would be have a sphere of radius 5 with its center 6 units below the plane.
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