Equation of Circle

A circle is the set of points equidistant from a point C(h,k) called the center. The fixed distance r from the center to any point on the circle is called the radius.

The standard equation of a circle with center C(h,k) and radius r is as follows:

(x - h) ² + (y - k) ² = r²

A circle is the set of points equidistant from a point C(h,k) called the center. The fixed distance r from the center to any point on the circle is called the radius.

The standard equation of a circle with center C(h,k) and radius r is as follows:

(x - h) ² + (y - k) ² = r²

A circle is the set of all points that are the same distance, r, from a fixed point. General Formula: X ² + Y² =r² where r is the radius

• Unlike parabolas, circles ALWAYS have X 2 and Y 2 terms. A circle is the set of points equidistant from a point C(h,k) called the center. The fixed distance r from the center to any point on the circle is called the radius.

  In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that(x - h) ² + (y - k) ² = r²

• This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram to the right, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x - a and y - b. If the circle is centered at the origin (0, 0), then the equation simplifies to

• The equation can be written in parametric form using the trigonometric functions sine and cosine as
• where t is a parametric variable, interpreted geometrically as the angle that the ray from the origin to (x, y) makes with the x-axis. Alternatively, a rational parameterization of the circle is:
• In homogeneous coordinates each conic section with equation of a circle is of the form.