What are the values of A, B, and C for rotating a line about the x-axis?

[Amebos]

Homework Statement

Let L be the line y=7, x=7z. If we rotate L about the x-axis, we get a surface whose equation is Ax^2 + By^2 +Cz^2=1

What are the values of A, B, and C?

Homework Equations

Listed above.

The Attempt at a Solution

Since y=7, my first point that I plugged into the surface area equation is (0,7,0), and the solution I get is B= 1/49. I also know that rotation of the line will hit the point (0,0,7), yielding C =1/49. Now both of those solutions are correct. However, I can't seem to solve A.

I know that x=7z. z = (1/49) so x=(7/49), or x=(1/7)
I plug these values in the equation to get the following:

A(1/7)^2 +1/49(7)^2 +1/49(7)^2 = 1
Simplification yields:

(1/49)A +1 +1 =1
Further simplification yields:
(1/49)A = -1

Now shouldn't the answer just be:

A= -49?

I must have made an arithmetic error or simply chosen the wrong value for x. If someone could please guide me in the right direction it would be most appreciated. Thanks to you guys in advance.

 

[Amebos]

Solved it.

I realized what my mistake was. I inserted the value for C into the place for the value of Z. Thus X=49 and the answer for A is

1/49^2