Question
Show that the equation of the plane that is tangent to the paraboloid$$z=\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$$at $\left(x_{0}, y_{0}, z_{0}\right)$ can be written in the form$$z+z_{0}=\frac{2 x_{0} x}{a^{2}}+\frac{2 y_{0} y}{b^{2}}$$
Step 1
The gradient is given by the partial derivatives of the function $z$ with respect to $x$ and $y$. The partial derivative of $z$ with respect to $x$ is $\frac{2x}{a^2}$ and the partial derivative of $z$ with respect to $y$ is $\frac{2y}{b^2}$. Show more…
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