the set of all points in a plane that are the same distance from a given point
The set of all points in a plane that are the same distance from a given point is called a circle
The set of all points in a plane that are the same distance from a given point is called a circle.
A circle is a geometric shape defined as a set of points equidistant from a fixed center point. The center of the circle represents the given point, and the distance from the center to any point on the circle is called the radius. Every point on the circle is exactly the same distance from the center.
In equation form, a circle can be represented by the equation (x – h)^2 + (y – k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius. This equation describes all the points (x, y) in the coordinate plane that satisfy the equation and lie on the circumference of the circle.
For example, if we have a circle with a center at (2, -3) and a radius of 5 units, the equation representing this circle would be (x – 2)^2 + (y + 3)^2 = 25. Any point (x, y) that satisfies this equation and lies on the circumference of the circle will be equidistant from the center point (2, -3).
Understanding circles and their properties is fundamental in various fields of mathematics, including geometry, trigonometry, and analytical geometry. Circles have unique properties, such as the fact that the diameter is twice the length of the radius and that all radii are perpendicular to the circumference at their endpoints. Circles also play a crucial role in many real-life applications, such as architecture, physics, and engineering.
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