Posted by sphere on Tuesday, August 23, 2011 at 11:56am.
First of all let me apologize if this is the wrong section; this is a review question from a Calculus III class, but it doesn't involve any actual calculus so I posted it here.
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 1:23pm
the 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
More 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 ...
- Finite Math - Fifty percent of students enrolled in calculus class have ...
- 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! ...