Problem

Consider the surface z = x2 + 4y2. (a) Find an equation for the plane that is tangent...

Consider the surface z = x2 + 4y2.

(a) Find an equation for the plane that is tangent to the surface at the point (1, −1, 5).

(b) Now suppose that the surface is intersected with the plane x = 1. The resulting intersection is a curve on the surface (and is a curve in the plane x = 1 as well). Give a set of parametric equations for the line in R3 that is tangent to this curve at the point (1, −1, 5). A rough sketch may help your thinking.

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