9.3. Circles http://www.ck12.org
9.3 Circles
Here you will formalize the definition of a circle, translate a conic from standard form into graphing form, and graph
circles.
A circle is the collection of points that are the same distance from a single point. What is the connection between
the Pythagorean Theorem and a circle?
Watch This
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/61851http://www.youtube.com/watch?v=g1xa7PvYV3I Conic Sections: The Circle
Guidance
A circle is the collection of points that are equidistant from a single point. This single point is called the center of
the circle. A circle does not have a focus or a directrix, instead it simply has a center. Circles can be recognized
immediately from the general equation of a conic when the coefficients ofx^2 andy^2 are the same sign and the same
value. Circles are not functions because they do not pass the vertical line test. The distance from the center of a
circle to the edge of the circle is called the radius of the circle. The distance from one end of the circle through the
center to the other end of the circle is called the diameter. The diameter is equal to twice the radius.
The graphing form of a circle is:
(x−h)^2 +(y−k)^2 =r^2
The center of the circle is at(h,k)and the radius of the circle isr. Note that this looks remarkably like the
Pythagorean Theorem.
Example A
Graph the following circle.
(x− 1 )^2 +(y+ 2 )^2 = 9
Solution: Plot the center and the four points that are exactly 3 units from the center.