# Thread: Plane Tangent to a Paraboloid.

1. ## Plane Tangent to a Paraboloid.

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

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

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

Then I would just apply:

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

Is this correct?

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

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

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

Then I would just apply:

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

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