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Line tangent to an intersection curve Consider the paraboloid z = x2 + 3y2 and the plane z = x + y + 4, which intersects the paraboloid in a curve C at (2, 1, 7) (see figure). Find the equation of the line tangent to C at the point (2.1, 7). Proceed as follows.
a. Find a vector normal to the plane at (2, 1, 7).
b. Find a vector normal to the plane tangent to the paraboloid at (2,1,7).
c. Argue that the line tangent to C at (2, 1, 7) is orthogonal to both normal
d. Knowing a point on the tangent line and the direction of the tangent line, write an equation of the tangent line in parametric form.
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Chapter 12 Solutions
Calculus: Early Transcendentals, 2nd Edition
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