Finding Spheres Tangent to Three Coordinate Planes: A Calc 3 Problem

  • Thread starter meadow
  • Start date
  • Tags
    Calc 3
In summary, to find each sphere that passes through the point (5,1,4) and is tangent to all three coordinate planes, you need to set up the equation with the center point (s,s,s) and the radius s, using the fact that the distance between a point and a coordinate plane is just one of its coordinates. Then, use the condition that the sphere passes through the given point to solve for s and find the equation of the sphere.
  • #1
meadow
19
0
The question asks to find each sphere that passes through the point (5,1,4) and are tangent to all three coordinate planes.
How would I set that up?
I have no problem finding the equation of a sphere when they give the center point and the radius, of course, but what do I need to know to find these equations?
 
Physics news on Phys.org
  • #2
OK, suppose your at the center point of the sphere. You look out and you should see each of the coordinate planes at equal distances because the sphere is tangent to each of them, so the vector from the center to the coordinate plane is perpendicular to the coordinate plane, meaning that the distance along this vector is the minimal distance and therefore "the" distance. Now, the distance between a point and a coordinate plane is just one of its coordinates. For example, the distance between a point and the x-y plane is just the z-coordinate. Now, since all of these distances are equal, the coordinates of the center must all be the same number. Call this number s, so the center is at (s,s,s). s must also be the radius of the sphere since it is the distance from the center to the surface. Now the the equation of the sphere is:
[tex](x-s)^2+(y-s)^2+(z-s)^2=s^2[/tex]
Use the last condition that it passes through the point (5,1,4) to solve for s and you're done.
 
  • #3
you're awesome

Thanks again. You are awesome.
 

What is "One more calc 3 problem"?

"One more calc 3 problem" refers to an additional problem or exercise in the field of Calculus 3 that students are asked to solve as part of their coursework or practice.

Why is it important to solve "One more calc 3 problem"?

Solving "One more calc 3 problem" helps students to reinforce their understanding of the concepts and techniques learned in Calculus 3. It also allows them to apply these skills to different types of problems, improving their problem-solving abilities.

How can I approach solving "One more calc 3 problem"?

There are various strategies for solving "One more calc 3 problem", but some common steps include understanding the problem, identifying the relevant concepts and formulas, and breaking the problem into smaller, more manageable parts. It is also helpful to draw diagrams or graphs and to check your work for accuracy.

What resources can I use to help me solve "One more calc 3 problem"?

Aside from your textbook and class notes, there are many online resources available for help with "One more calc 3 problem". These include video tutorials, practice problems, and discussion forums where you can ask for assistance from fellow students or instructors.

How can I improve my performance in solving "One more calc 3 problem"?

Consistent practice and seeking help when needed are key to improving your performance in solving "One more calc 3 problem". It is also important to review your mistakes and understand where you went wrong, so you can avoid making the same errors in the future. Additionally, staying organized and managing your time effectively can also contribute to better performance.

Similar threads

Replies
10
Views
406
  • Introductory Physics Homework Help
Replies
9
Views
699
  • Introductory Physics Homework Help
Replies
6
Views
814
  • Electromagnetism
Replies
2
Views
280
  • Introductory Physics Homework Help
Replies
17
Views
370
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
585
  • Introductory Physics Homework Help
Replies
12
Views
4K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
487
Back
Top