Please help me get started on the following problem. Find an equation of the sphere with center (2,-1,-3) satisfying the given condition: Tangent to the xy-plane.
Stacey Warren - Expert brainly.com
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If I recall correctly, a sphere with center \((h,k,l)\) has the equation
where \(r\) is the radius of the sphere.
You know the center, so you just have to find the radius of the sphere. It's tangent to the xy-plane, so you have to find the distance from the center (2,-1,-3) to this point's projection on the xy-plane, which would be (2, -1, 0).
How did you determine the point (2,-1,0)?
Forgive the poor drawing. It's a bit tough in three dimensions.|dw:1370989801438:dw|
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For every point in the xy-plane, there is no z-coordinate. In 3-space, you let \(z=0\), which (in the drawing) would move you "up" 3 units to the point (2, -1, 0):
But we're dealing with a sphere
What's your point? A sphere is 3-dimensional, isn't it?
Perhaps you're confused by the lack of a sphere in the drawing? I only drew the sphere's center for simplicity, since that's all the information you really need. The center's distance from the xy-plane is what's needed to find the radius, and thus the equation of the sphere itself, as I said before.
ok so r^2=9
and is r positive or negative 3? Or is that irrelevant?