Page 4 - CONIC SECTION - EBOOK._Neat

Conic section

CIRCLE

A circle is a geometrical shape, and is not of much use in algebra, since the equation of a
circle isn't a function. But you may need to work with circle equations in your algebra
classes.

In "primative" terms, a circle is the shape formed in the sand by driving a stick (the
"center") into the sand, putting a loop of string around the center, pulling that loop taut
with another stick, and dragging that second stick through the sand at the further extent
of the loop of string. The resulting figure drawn in the sand is a circle.

In algebraic terms, a circle is the set (or "locus") of points (x, y) at some fixed
distance r from some fixed point (h, k). The value of r is called the "radius" of the circle,
and the point (h, k) is called the "center" of the circle.

The "general" equation of a circle is:

x + y + Dx + Ey + F = 0
2
2
The "center-radius" form of the equation is:

(x – h) + (y – k) = r
2
2
2
...where the h and the k come from the center point (h, k) and the r comes from the
2
radius value r. If the center is at the origin, so
(h, k) = (0, 0), then the equation simplifies to x + y = r .
2
2
2

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