Thread: Intersection of two surfaces

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

The question:
For what values of 'a' do the surfaces and not intersect?

My attempt:
I rearranged the first equation like so:


Then equated it with the other:


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

I then solved for a:


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!

This equation has no solution when the discriminant is negative

Ahh that makes sense, thank you!

Originally Posted by Glitch

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

The question:
For what values of 'a' do the surfaces and not intersect?

My attempt:
I rearranged the first equation like so:


Then equated it with the other:


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

I then solved for a:

This is the "wrong way". Solve the equation for z, not a. That is a quadratic equation for z so there will be no real number solution for z if the "discriminant" ( ) is negative.

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!