Thursday

April 2, 2015

April 2, 2015

Posted by **sphere** on Tuesday, August 23, 2011 at 11:56am.

If I have a sphere with center (2,-10,4) and radius 10 what is:

the intersection with the yz plane?

the intersection with the xy plane?

I get tripped up with geometry in more than 2 dimensions so I'm confused as how to handle this.

Should I treat the "omitted plane" (my term for lack of a better word) value as zero? If so does that change the radius? I'm guessing not given that the distance formula for a circle or a sphere is equal to r^2.

So for yz would I say

(y+10)^2 + (z-4)^2 = 100

And if so, how do I find the yz plane intersection from that? I know I've done this before but I don't recall how to do it.

- geometry -
**Reiny**, Tuesday, August 23, 2011 at 1:23pmthe equation of the sphere is

(x-2)^2 + (y+10)^2 + (z-4)^2 = 100

so in the xz plane: y = 0

(x-2)^2 + 100 + (z-4)^2 = 100

(x-2)^2 + (x-4)^2 = 0

conclusion: the yz plane just touches the sphere.

for xy plane , let z=0

(x-2)^2 + (y+10)^2 + 16 = 100

(x-2)^2 + (y+10)^2 = 84

Visualize the sphere having a slice cut off, and you are looking at the surface of the cut.

Wouldn't that be a circle?

And unless the cut is made through the middle of the sphere, wouldn't that circle have a radius less than 10 ?

So for my answer of (x-2)^2 + (y+10)^2 = 84, the centre of that surface would be (2, -10,0) and the radius of the cut surface would be √84

you had the right idea, but you just dropped the whole bracketted term, you should have just let the y=0

**Answer this Question**

**Related Questions**

Calculus Precalculus - Answer the calculus question about Point P, 45 mph, etc. ...

Calculus - The question is, if f(x) is equal to the series from n to infinity of...

Bob Pursley - Bob: Thank you for answering my Chemistry question. I apologize ...

Statistics - A class has 3 sections. Here is a summary of the scores on the ...

calculus - i'm having trouble with a problem in my calc class...it isn't really ...

CALCULUS EXAM REVIEW - Hi, my exam is tomorrow and I'm here with my girlfriend ...

Calculus - Need an answer to this Calculus Question. I keep getting this type of...

Algebra - In an interview of 50 math majors, 12 liked calculus and geometry 18 ...

Lord of the Flies - I apologize, I posted the wrong question on my last post! ...

Math - Hi, I have to do a project on the Shell Method in my Geometry class. I ...