Question

Calc 3? Describe the geometry of the set points whose coordinates x,y,z satisfy the equation x^2+y^2+z^2+4x+2y-6z-22=0?

Answer 1

doing quadratic surfaces, are we?

Answer 2

Try completing the square

you will get it in this form


(x-a)^2 +(y-b)^2 +(z-c)^2 =k

so it's a sphere

Answer 3

Any ideas?

Answer 4

Ohh I see I've that before I didn't know if that was what it meant by describing thanks!

Answer 5

"geometry of the set points" is way of asking what shape

Answer 6

What happens if it's only like (x-a)^2 +(y-b)^2=K

Answer 7

then it would be a circle

Answer 8

what does a and b stand for? the transformation it shifts about? and K is the radius right just making sure I understand it right

Answer 9

yes , you are right

Answer 10

okay thanks a lot!

Answer 11

Calc 3 will get a lot more interesting after this stuff

Answer 12

Hey sorry I have one more question, it says show that the intersection of that equation with yz is a circle, does that mean that I make x as 0?

Answer 13

yes,

Answer 14

b/c x=0 on entire y-z plane

Answer 15

so the equation I got was (x+2)^2 + (y+1)^2 + (z+3)^2 = 34 and I'd make it zero so I'd get just (y+1)^2 + (z+3)^2 = 30

Answer 16

ohh I see yeah okay thanks

Answer 17

Okay last thing I swear.... I just want to make sure I'm doing this right b/c I have a test tmr it's just practice

Answer 18

it says describe the intersection of the obj in part a with object in part c..

Answer 19

this is part a : (x+2)^2 + (y+1)^2 + (z+3)^2 = 34 and part c (x+2)^2+(y+1)^2=11.. what does that mean ?

Answer 20

do I combine them? I'm suppose to get 2 circles?

Answer 21

one is sphere while other is circle

Answer 22

Yeah that's what I thought but then it says I'm suppose to obtain two circles. So I assumed that intersection meant somehow they were equal

Answer 23

let me try to plot them

Answer 24

Can't get it to work if I put them together (x+2)^2 and (y+1)^2 cancels

Answer 25

you are supposed to obtain two circle?

Answer 26

It would just be a circle cutting through the sphere

Answer 27

well you know how if a sphere intersects with a plane you get a circle? I'm assuming if a circle intersects a sphere you get two circles??

Answer 28

I don't know it says on the sheet, do you have any ideas how to show that?