Cartesian equation

In a plan, reported to a Cartesian reference mark, the solutions of an equation $E$ of unknown factors $x$ and $y$ can be interpreted like a whole of points $M\; \backslash \; left\; (X;\; there\; \backslash \; right)$ of this plan. When these solutions form a curve, it is said that $E$ is a Cartesian equation or reduced equation of this curve.

Definition

In a space with $n$ dimensions, a Cartesian equation is an equation of the form $f\; (X)\; =0$ where $f$ is a function of class $\backslash \; mathcal\; \{C\}\; ^1$, of $\backslash \; mathbb\; \{R\}\; ^n$ in $\backslash \; mathbb\; \{R\}$.

• In the plan the equation is written $f\; (X,\; there)\; =0$;
• In space the equation is written $f\; (X,\; there,\; Z)\; =0$.

Equations of curves in the plan

• Equation of right-hand side: $ax\; +\; by\; +\; C\; =\; 0$, where $a$, $b$ and $c$ are real constants .
  It is a line of directing vector $\backslash \; vec\; \{U\}\; (-\; B;\; a)$.

• Equation of a circle: $\backslash \; left\; (x-x\_0\; \backslash \; right)\; ^2+\; \backslash \; left\; (there\; there\; \_0\; \backslash \; right)\; ^2=c^2$, where $x\_0$, $y\_0$ and $c$ are real constants, $c>0$.
  It is a circle of center $\backslash \; left\; (x\_0,\; y\_0\; \backslash \; right)$ and of ray $c$.

Equations of surfaces in space

• Equation of a plan: ax + by + cz + D = 0

• Equation of a sphere of center M (has, B, c) of ray R: (x-a) ² + (y-b) ² + (z-c) ² = R ²

See too

• analytical Geometry
• vectorial Geometry
• Location in the plan and space

Random links:

Messiah (televised series) | Center mutual credit Is Europe | Albatross with black feet | Shock To absorb | Hemipus | Kari_Lehtonen

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org