# Analytic Geometry

• I. N. Bronshtein
• K. A. Semendyayev

## 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

Sine Cane Dinates Cylin

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### Notes

1. (1).
The angle φ is positive, when the axes rotate counterclockwise.Google Scholar
2. (1).
It can happen that the given equation F(x, y) = 0 is not satisfied by any real point of the plane (for example, x2 + y2+ 1 = 0, y = ln (1 − x2 − cosh x)). Then we conditionally say that the given equation represents an imaginary curve.Google Scholar
3. (1).
In the following formulas containing coordinates, the ellipse is assumed to be given by its canonical equation.Google Scholar
4. (1).
In the formulas containing coordinates, the hyperbola is assumed to be given by its canonical equation.Google Scholar
5. (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
6. (1).
The x axis is assumed to be directed to the right and the y axis — upwards.Google Scholar
7. (2).
In the formulas containing coordinates, the parabola is assumed to be given by its canonical equation.Google Scholar
8. (1).
Expressed in a certain units of measure.Google Scholar
9. (1).
For the orientation of a triple of axes see p. 617.Google Scholar
10. (1).
For the triple (box) product of vectors see p. 618.Google Scholar
11. (2).
For the scalar product of vectors see p. 616.Google Scholar
12. (1).
A condition for two planes to be parallel is given on p. 269.Google Scholar
13. (2).
For reduction of a general equation of a plane to the normal form see p. 263.Google Scholar
14. (3).
For the scalar product of vectors see p. 616.Google Scholar
15. (1).
For products of vectors, see p. 616.Google Scholar
16. (1).
For products of vectors, see p. 616.Google Scholar
17. (1).
For general equations of surfaces of the second degree, see p. 275.Google Scholar
18. (1).
We assume here aik = aki.Google Scholar