Equation of Circle center Origin
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Theorem
The circle with radius $R$ whose center is at the origin expressed in Cartesian coordinates is given by the equation:
- $x^2 + y^2 = R^2$
Proof
From Equation of Circle in Cartesian Plane, the equation of a circle with radius $R$ and center $\tuple {a, b}$ expressed in Cartesian coordinates is:
- $\paren {x - a}^2 + \paren {y - b}^2 = R^2$
Setting $a = b = 0$ yields the result.
$\blacksquare$
Sources
- 1914: G.W. Caunt: Introduction to Infinitesimal Calculus ... (previous) ... (next): Chapter $\text I$: Functions and their Graphs: $1$. Constants and Variables
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $1$. To find the equation of a circle of radius $r$ with its centre at the origin
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{III}$: Gentleman, Soldier and Mathematician
- 1959: T.J. Willmore: An Introduction to Differential Geometry ... (previous) ... (next): Chapter $\text{I}$: The Theory of Space Curves: $1$. Introductory remarks about space curves
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.6$: How Archimedes Discovered Integration
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): locus (plural loci)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): locus (plural loci)
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Descartes