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Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations). z = 4 - 2x2 - y2; (2, 2, -8) and (-1, -1, 1)

Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations). z = 4 - 2x2 - y2; (2, 2, -8) and (-1, -1, 1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations).

z = 4 - 2x2 - y2; (2, 2, -8) and (-1, -1, 1)

Expert Solution
Step 1 To find:

An equation of the plane tangent to the following surfaces at the given points (two planes and two equations):

z = 4 - 2x2 - y2; (2, 2, -8) and (-1, -1, 1).

 

Step 2 Concept used:

Equation of the tangent to surface z=f(x,y).

fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0)-(z-z0)=0

Step 3

Here, fx,y=4 - 2x2 - y2

Differentiate fx,y with respect to x.

fx=0-22x-0=-4x

Differentiate fx,y with respect to y.

fy=0-0-2y=-2y

 

 

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