Equations and curves
Equations and curves [ edit ] Main articles: Solution set and Locus (mathematics) In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus . For example, the equation y = x corresponds to the set of all the points on the plane whose x -coordinate and y -coordinate are equal. These points form a line , and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections , and more complicated equations describe more complicated figures. [17] Usually, a single equation corresponds to a curve on the plane. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation...