Question

Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x^2 + y^2 and the ellipsoid 5x^2 + 4y^2 + 2z^2 = 17 at the point (-1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Name: find parametric equations for the tangent line to the curve of intersection of the paraboloid z x2 y2 and the ellipsoid 5x2 4y2 2z2 17 at the point 1 1 2 enter your answer as a comma separat 68188
Uploaded: 2022-05-10T08:08:09-08:00
Duration: 3 min 55 s
Channel: Sri K
Description: find parametric equations for the tangent line to the curve of intersection of the paraboloid z x2 y2 and the ellipsoid 5x2 4y2 2z2 17 at the point 1 1 2 enter your answer as a comma separat 68188

          Find parametric equations for the tangent line to the curve of intersection of the paraboloid 
z = x^2 + y^2
and the ellipsoid 
5x^2 + 4y^2 + 2z^2 = 17
at the point 
(-1, 1, 2).
(Enter your answer as a comma-separated list of equations.
Let x, y, and z be in terms of t.)

Added by Thomas M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

05/10/2022

Step 1

The gradient vector of the paraboloid z = x^2 + y^2 at (-1, 1, 2) is given by ∇f = <∂f/∂x, ∂f/∂y, ∂f/∂z> = <-2, 2, 1>. The gradient vector of the ellipsoid 5x^2 + 4y^2 + 2z^2 = 17 at (-1, 1, 2) is given by ∇g = <∂g/∂x, ∂g/∂y, ∂g/∂z> = <-10, 8, 4>. ** Show more…

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Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x^2 + y^2 and the ellipsoid 5x^2 + 4y^2 + 2z^2 = 17 at the point (-1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)