Circle

Definition

A circle is a 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.

5 Must Know Facts For Your Next Test

1. The standard form of the equation for a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius.
2. Circles can be part of systems of nonlinear equations, often intersecting with other circles or parabolas.
3. To solve for intersections involving circles, you typically substitute one equation into another and solve for $x$ and $y$.
4. The general form of a circle's equation is $Ax^2 + Ay^2 + Dx + Ey + F = 0$, which can be converted to standard form by completing the square.
5. Identifying whether two circles intersect involves comparing their radii and the distance between their centers.

Review Questions

• What is the standard form of a circle's equation?
• How do you find the intersection points between a circle and another curve?
• What steps are involved in converting a general form equation of a circle to its standard form?

Related terms

Ellipse:

A set of all points in a plane such that the sum of their distances from two fixed points (foci) is constant.

Radius:

The distance from the center of a circle to any point on its circumference.

Center:

The fixed point equidistant from all points on a circle.