$p=(2,-1,z_0)$ lies on the surface $ z- \ln(2x^2+y^2)+\ln 3=0$, we need to determine $z_0$ and equation for tangent plane to the surface at $p$. $z_0-\ln(4+1)+\ln 3=0\Rightarrow z_0=\ln \frac{5}{3}$. Could anyone help me the next step? Thanks!

Let $A=\{a_{ij}\}$ be a $n\times n$ symmetric and positive definite matrix, it's well known that, for some $n$-vector $x$, $x'Ax$ is a scalar: $$ x'Ax=\sum_{i=1}^n\sum_{j=1}^n a_{ij}x_i x_j. $$ What can be said about the quadratic form $x'A^{-1}x$? Is it possible to write is as a function of the...