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I have a surface given by the equation $f(x,y,z)=0$ and need to find the Tangential plane on a given point $p$.

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$$ \frac{\partial f}{\partial x} (x - p_x) + \frac{\partial f}{\partial y} (y - p_y) + \frac{\partial f}{\partial z} (z - p_z) = 0 $$

is the equation of the tangent plane to the surface defined by $f(x,y,z)=0$ at the point $p = (p_x, p_y, p_z)$. The partial derivatives are evaluated at $p$.

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