Hey guys. So I'm taking Calc III and Differential equations this summer simultaneously over 8 weeks and 4 days in I'm kind of losing my mind a bit hah. That being said, I'd like to run a problem by you and see if I'm just making a stupid mistake or if my professor is ignoring a potential error in his assigned homework (this is graded which is why I'm being careful with it).


So the question states:

Prove the following equation represents a sphere in R^3. Find its center and radius.

x^2 + y^2 + z^2 -6x + 4y +2z = -17



Below is the work I've done on grouping and completing the square. I keep getting a negative value on the right side for the r^2 term so I'm not quite sure where I'm going wrong.



x^2 -6x + y^2 +4y + z^2 +2z = -17

(x-3)^2 + (y+2)^2 + (z+1)^2 = -17 + 9 + 4 + 1

(x-3)^2 + (y+2)^2 + (z+1) ^2 = -3


Any insight? Thank you!!

This post was edited by BAJuicer on May 12 2016 05:20pm

Doesn't graph as a sphere for me. Are you sure you took the problem down correctly?

There is no mistake in your calculations. The previous equation represents the empty set.

You can eventually consider that the empty set is a sphere with a negative radius...
But I guess the equation should have been +17 instead of -17 !

Hah that was my first guess -- that I copied something down incorrectly. But I've checked 10 times over and that's how it was written on his sheet.



Ah ok... so as far as someone just starting calc III, there is no real way for me to solve it then?

It's frustrating because I emailed the professor, asked him to politely look at this problem and the work I had done, and his response was, "my books have no errors." He comes off as very arrogant and condescending. I get it, he's a smart dude, PhD and all of that, but I don't understand that mindset as a teacher.

It must be +17.

https://www.wolframalpha.com/input/?i=x^2+%2B+y^2+%2B+z^2+-6x+%2B+4y+%2B2z+%3D+17