At what point on the paraboloid [tex] y=x^2+z^2 [/tex] is the tangent plane parallel to the plane [tex] x+2y+3z=1 [/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

Tangent plane equation is...

[tex] Fx(X,Y,Z,)(x-X)+Fy(X,Y,Z)(y-Y)+Fz(X,Y,Z)(z-Z)=0; for x^2+z^2-y=0 [/tex]

My attempt at the problem...

First I found the unit normal for the plane I'm trying to match [tex] x+2y+3z=1 [/tex]

so.. [tex] \sqrt{1^2 + 2^2 + 3^2} = \sqrt{14}[/tex]

to the unit normal is [tex] \frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}, [/tex]

now I set that equal to the tangent plane equation and solve for the the point right? So...

[tex] 2x(X,Y,Z,)(x-X)-1(X,Y,Z)(y-Y)+2z(X,Y,Z)(z-Z)=\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}[/tex]

Am I on the right track?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Setting a tangent plane parallel to another plane-Cal III

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