Analytical Geometry Grade 12 Exercises: Questions and Answers pdf: In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.

## Analytical Geometry Grade 12 Exercises/ Studyguides: Questions and Answers Downloadable pdfs

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* Analytical Geometry Study Guide for Grade 12*:

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## Equations and curves

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.

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 *x*^{2} + *y*^{2} = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations. The equation *x*^{2} + *y*^{2} = *r*^{2} is the equation for any circle centered at the origin (0, 0) with a radius of r.

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