Calc 3 problem...
Find the slope of the tangent to the curve of the intersection of the cylinder 6z=3 sqrt(20-x^2) and the plane y=9 at the point (2,9,2)

Question

Calc 3 problem...
Find the slope of the tangent to the curve of the intersection of the cylinder 6z=3 sqrt(20-x^2) and the plane y=9 at the point (2,9,2)

empty · Answer

what have you done so far?

anonymous · Answer

Nothing - not sure how to even start it

anonymous · Answer

I'm guessing to start off with finding an equation of the tangent line..

anonymous · Answer

Don't know how to get slope or how the "y=9" fits into this

anonymous · Answer

First note that this isn't really a cylinder because its cross-sections are not circular, but rather elliptical. (Still a quadric surface, though.)
$$6z=3\sqrt{20-x^2}~~\implies~~4z^2+x^2=20$$
Let's draw this in the $x$-$z$ plane:
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