Find a vector function describing the curve of intersection of the two surfaces:

The cone z = sqrt(x^2 + y^2), and
the plane x + y + z = 1.

Question

Find a vector function describing the curve of intersection of the two surfaces:

The cone z = sqrt(x^2 + y^2), and 
the plane x + y + z = 1.

anonymous · Answer

Is it recommended that I square both sides of the 1st equation, first? Then parametrize?

anonymous · Answer

You could. I did that but still going nowhere

anonymous · Answer

it's plane cutting the cone at an angle but i'm still trying to figure out if it's a circle, ellipse, or hyperbola

anonymous · Answer

That would be quite helpful to know...I'll keep plugging away at it. I really appreciate your assistance!

anonymous · Answer

well, it's a hyperbola after using my computer to graph it.

anonymous · Answer

Sweet! Thanks. What program are you using?

anonymous · Answer

well, it's online. The result is a hyperbola that is rotated at an angle, i'm guessing 45 degrees http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/CalcPlot3D.htm

anonymous · Answer

That helps. Thanks again!

anonymous · Answer

here is diagram:

anonymous · Answer

Precisely what I got! At least I know I'm on the right path. Nasty little problem though.

anonymous · Answer

yeah, it's hard to visualize graphs in 3D without computer aid. Even if it's something as simple as this