This is from a Vector Calculus course, so I hope it belongs in this section.Note:

The question:

For what values of 'a' do the surfaces $\displaystyle x^2 + y^2 + (z - 1)^2 = 1$ and $\displaystyle a(z+1)^2 = x^2 + y^2, (z \ge -1)$ not intersect?

My attempt:

I rearranged the first equation like so:

$\displaystyle x^2 + y^2 = 1 - (z - 1)^2$

Then equated it with the other:

$\displaystyle a(z+1)^2 = 1 - (z - 1)^2$

Usually I'd solve for z to find the conditions for the intersection, but we have two variables now.

I then solved for a:

$\displaystyle a = \frac{1 - (z - 1)^2}{(z+1)^2}$

So when z = -1, 'a' isn't defined. I then substituted this value into the very first equation to see what happens, but I just get the origin point.

I don't think I'm doing this correctly. Any assistance would be great!