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Numerade Educator

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Problem 23 Easy Difficulty

Find equations of the spheres with center $ (2, -3, 6) $ that touch (a) the $ xy $-plane, (b) the $ yz $-plane, (c) the $ xz $-plane.

Answer

(a) $(x-2)^{2}+(y+3)^{2}+(z-6)^{2}=36$
(b) $(x-2)^{2}+(y+3)^{2}+(z-6)^{2}=4$
(c) $(x-2)^{2}+(y+3)^{2}+(z-6)^{2}=9$

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Video Transcript

in the human problem, we have to find equations offs affairs for the given three conditions. First off, all we will write standard equation off. So fair which is X minus mhm scared. Bless Why minus be scared less Yeah. Z minus C squared equals are scared here a coma? Be calm. Asi is the center off. So fear and are is you just radius in the human problem center off disappear is equal toe to common minus three Coma six So by putting the values off ABC in standard equation office affair we will get eggs minus toe Scared Bless Why bless three Scared less Z minus six. Scared equals are scared. Let's call it equation one now in first part off the problem does a fear. Dutch is X y learn So the coordinates off point off contact off. So fair and ex wife land will be two comma minus three coma zero since this point lies on this affair, so it's coordinators must satisfy the equation off Sophia. So by putting x equal toe do why equals minus three and Z equals zero in equation one. We will get radius off this affair. R equals six for our equals six equals in one becomes X minus toe scared bloods y les three scared less Z minus six square equals six Scared. This is equal to X minus two. Scared less. Why bless? Three. Scared less the mine. Six Scared equals 36. This is the equation off. So fair. That's his X Y plan. Now in part, be off the problem. The severe touches. Why the Lynn? Why they plan in this case, the coordinates of the point of contact offs Affair and Vaezi plan We will be zero common minus three coma six By putting the values off X y and see in equation one, we will get radius off the severe uh equals two for r equals two equals in one becomes X minus two Scared Bless y bliss three Scared Bless Z minus six. Scared because toe scared This is equal to X minus two Scared plus y pless three scared plus Z minus six. Scared because floor this is the equation off. So fear touches Why the plan? No, in part, see off the problem. Disappear, disappear, touches xz plant. In this case, the coordinates off point of contact will be do zero six. So by putting these values in the question one, we will get radius after severe R equals three for our equals. Three it was in one becomes X minus two scare. Bless wife Bless three square less Z minus six. Scare equals three Scared. This is equal to X minus two Scared plus y last three squared less Z minus six squared equals night. This is the equation offs affair. This is Dick with an office affair catches exit plan.