- A straight line segment between two points on a curve.
- A curved planar figure, all points of which are the same
distance from a fixed point called the center.
- 1) A line segment connecting two points on a circle, and
passing through its center. 2) Twice the radius (of a
- 1) A line segment from a circle to its center. 2)The
distance from any point on a circle to its center.
- Geometrically, a circle can be defined as:
Given a fixed point C, a circle is the figure formed from all
points P for which PC is constant.
- The fixed point is called the center.
- Analytically, a circle can be defined as:
Given a constant r, a circle is the locus of all points
(x, y) for which
x2 + y2 = r2
- The geometric definition and the analytic definition are
equivalent, and will produce the same figure for center
- A line segment from (x, y) to (0, 0), is called a
radius of the circle.
- A line segment from (x, y) to (-x, -y), is called a
diameter of the circle.
- These terms are also used to refer to the lengths of these line
- A line segment from (x1, y1) to
(x2, y2) is called a chord of the
- A circle (in the standard form) intercepts the x axis at
(r, 0) and (-r, 0).
- A circle (in the standard form) intercepts the y axis at
(0, r) and (0, -r).
- The excentricity e of a circle is
- For all circles, e = 0;
- The equation
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
will describe a circle if the discriminate,
B2 - 4AC,
is equal to 0.
- A circle can also be defined parametrically:
Given a constant r and a parameter θ, a circle is the
locus of all points (x, y) for which
x = r cos θ, and
y = r sin θ
- A circle can also be defined in polar coordinates
Given a constant r greater than 0, a circle is the locus of
all points (ρ, θ) for which
|| Planet Math
|| Math Now
|| Analytic Geometry Index
/ Circle / Circle /