Circles: Standard and General Equation, Parametric Form A circle is defined as the set of all points in a plane that are equidistant from a fixed point call...
Circles: Standard and General Equation, Parametric Form
A circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.
Standard Equation:
The standard equation of a circle with center at the origin is:
where:
(h, k) is the center point
r is the radius
Examples:
Parameter Form:
The parameter form of a circle is given by the equation:
where:
(h, k) is the center point
r is the radius
Examples:
Key Differences between Standard and Parameter Form:
The standard equation is a specific equation that represents a circle as a set of points.
The parameter form is a more general equation that can be used to represent a circle for any center point and radius.
The parameter form is more convenient for solving geometric problems and finding the area and circumference of a circle