ABSTRACT
Quadratic forms occur naturally in physics, economics, engineering (control theory), and analytic geometry (quadratic curves and surfaces). Particularly, recall that the equation (quadratic form) of a central quadratic curve in a plane, after translating the origin of the rectangular coordinate system to the centre of the curve, appears as q 2 ( x , y ) = ( x , y ) a b b c x y = a x 2 + 2 b x y + c y 2 = d . $$ q_{2} (x,~y) = (x,~y)\left( {\begin{array}{*{20}c} a & b \\ b & c \\ \end{array} } \right)\left( {\begin{array}{*{20}c} x \\ y \\ \end{array} } \right)~ = ax^{2} + 2bxy + cy^{2} = d. $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315208657/c3a398e7-9861-47a8-b5b5-8b0c24135fcb/content/math22_1.tif"/>
