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Numerade Educator

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Problem 14 Medium Difficulty

Find an equation of the sphere with center $ (2, -6, 4) $ and radius 5. Describe its intersection with each of the coordinate planes.

Answer

$(x-2)^{2}+(y+6)^{2}+(z-4)^{2}=25$

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Video Transcript

we have a question and this we need to find a question of the sphere with center to common minus six comma four. So center if this is fair, so center is being given as two comma minus 64 and radius is fight. Okay so question of his fear will be equal to x minus H. Hold square plus y minus K. Why minus f. Whole square plus zed minor G Whole square equal to our square. So X minus the X coordinate of center to hold square plus Y minus -6 Whole Square. It was at -4. Hold Squire equal to five square. Let us open it up. This will be access squared platform minus four X. Plus. Why? This will become Y plus six or why square Plus 36 plus 12. Y Plus that square plus 16 -8. said Equal to 25. Let's write it like that's a Squire plus Y squared Because that is Square -4 x less 12 y minus eight. Set and four plus 36 40 plus. Uh 1640 plus 16 is 56 plus 31 equal to zero. This is the required a question of this fear. Thank you