# Plane Tangent to a Paraboloid.

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• Aug 12th 2009, 01:55 PM
adkinsjr
Plane Tangent to a Paraboloid.
- I need to find at what point on te paraboloid $y=x^2+z^2$ is the tangent plane parallel to the plane $x+2y+3z=1$.

I can handle most of this problem myself, but I need to know if this is the correct equation to start with:

$f(x,y,z)=x^2-y+z^2$

Then I would just apply:

$f_x(x_o,y_o,z_o)(x-x_o) + f_y(x_o,y_o,z_o)(y-y_o) +f_z(x_o,y_o,z_o)(z-z_o)=0$

Is this correct?
• Aug 12th 2009, 05:24 PM
luobo
Quote:

Originally Posted by adkinsjr
- I need to find at what point on te paraboloid $y=x^2+z^2$ is the tangent plane parallel to the plane $x+2y+3z=1$.

I can handle most of this problem myself, but I need to know if this is the correct equation to start with:

$f(x,y,z)=x^2-y+z^2$

Then I would just apply:

$f_x(x_o,y_o,z_o)(x-x_o) + f_y(x_o,y_o,z_o)(y-y_o) +f_z(x_o,y_o,z_o)(z-z_o)=0$

Is this correct?

Should be very simple and direct. While this is correct, but not necessary to apply this.