Find an equation of the tangent plane to the parametric surface x=−2rcosθ, y=−2rsinθ, z=r at the point (−22–√,−22–√,2) when r=2, θ=π/4.

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10-08-2022
Mathematics

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Find an equation of the tangent plane to the parametric surface x=−2rcosθ, y=−2rsinθ, z=r at the point (−22–√,−22–√,2) when r=2, θ=π/4.

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anshumanaryan799 anshumanaryan799 · Answer 1 · 2022-08-15T14:22:30+02:00

The equation of the tangent plane to the parametric surface is 3x + 2y + 6 root2z = 0.

A tangent to a curve was a line that just touched the curve at that point and was "parallel" to the curve at that point. A well-tangent plane to a surface is a plane that just touches the surface at that point and is "parallel" to the surface at that point.

The tangent plane to surface S at point P0 includes all tangents to curves in S that pass through P0. For a plane tangent to a surface to exist at a point on that surface, it is sufficient if the function defining the surface is differentiable at that point.

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