## Abstract

**Coordinates**. The position of an arbitrary point in the plane can be determined by aid of a coordinate system. The numbers which determine the position of a point are called its *coordinates*. The most frequently used are Cartesian rectangular coordinate system and polar coordinate system.

## Keywords

Radius Vector Polar Axis Analytic Geometry Elliptic Cylinder Canonical Equation
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## Notes

- (1).The angle φ is positive, when the axes rotate counterclockwise.Google Scholar
- (1).It can happen that the given equation
*F*(*x*,*y*) = 0 is not satisfied by any real point of the plane (for example,*x*^{2}+*y*^{2}+ 1 = 0,*y =*ln (1 −*x*^{2}− cosh*x*)). Then we*conditionally*say that the given equation represents an imaginary curve.Google Scholar - (1).In the following formulas containing coordinates, the ellipse is assumed to be given by its canonical equation.Google Scholar
- (1).In the formulas containing coordinates, the hyperbola is assumed to be given by its canonical equation.Google Scholar
- (1).Only one of two conjugate diameters intersects the hyperbola (this one for which
*k*<*b*/*a*). The chord obtained here is a diameter in a more restricted sense; it is bisected by the centre.Google Scholar - (1).
- (2).In the formulas containing coordinates, the parabola is assumed to be given by its canonical equation.Google Scholar
- (1).Expressed in a certain units of measure.Google Scholar
- (1).For the orientation of a triple of axes see p. 617.Google Scholar
- (1).For the triple (box) product of vectors see p. 618.Google Scholar
- (2).For the scalar product of vectors see p. 616.Google Scholar
- (1).A condition for two planes to be parallel is given on p. 269.Google Scholar
- (2).For reduction of a general equation of a plane to the normal form see p. 263.Google Scholar
- (3).For the scalar product of vectors see p. 616.Google Scholar
- (1).For products of vectors, see p. 616.Google Scholar
- (1).For products of vectors, see p. 616.Google Scholar
- (1).For general equations of surfaces of the second degree, see p. 275.Google Scholar
- (1).

## Copyright information

© Verlag Harri Deutsch, Zürich 1973