The Equation X^2 + Y^2 = R^2 And Its Representation Of A Circle On A Cartesian Coordinate System

x^2 + y^2 = r^2

equation of a circle centered at (0, 0) with the radius r

The equation x^2 + y^2 = r^2 represents a circle of radius r centered at the origin (0, 0) on a Cartesian coordinate system.

Here’s how to understand it:

– The equation involves two variables, x and y, which represent coordinates on a 2D plane.
– The left-hand side of the equation sums the squares of x and y, which is equivalent to finding the squared distance of a point (x, y) from the origin (0, 0). This is known as the Pythagorean theorem.
– The right-hand side of the equation represents a constant radius squared; r^2 is the squared length of a line segment from the center of the circle to any point on the perimeter.
– Therefore, any point (x, y) that satisfies the equation is located on the circle’s circumference, as its distance from the origin is equal to r. Conversely, any point outside the circle (x^2 + y^2 > r^2) is farther from the origin than r, and any point inside the circle (x^2 + y^2 < r^2) is closer to the origin than r.

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