Values of A so that 2 surfaces intersect HELP!

U

Unununium111

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Jan 20, 2011
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Hey there, it's been a while since I have taken calc and I can't seem to get this calc 3 stuff. Here goes... Find the values for A such that the following two sufaces intersect: x + 4y^2 + z^2 = 1 and x + y + z = A

So this has to be related to distance formula? I am oblivious as to where to start.

Thanks in advance...
 
I think it's easiest to solve the second equation for x, and then substitute A-y-z in for x in the first equation. What you get is an equation that looks like its graph will be an ellipse. But some values of A may give an ellipse while others will give no solution. To figure out which values of A will lead to a nonempty graph put the equation in standard form by completing the square twice.
 
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