Analytic geometry

Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.

General Formula: X ² + Y ²=r² where r is the radius

• Unlike parabalas, circles ALWAYS have X ² and Y ² terms.
• X² + Y²=4 is a circle with a radius of 2 ( since 4 =2²)
• Remember that a circle is a locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle.

Find the equation of a circle having endpoints (3,7) and (5,-2).

center:  (3-5/2, 7-2/2)=(-1,5/2)

D:  square root of (-5-3)^2+(-2-7)^2

=square root of 64+81

=square root of 145

=12.04

=12.04/2=6.02

(x-h)^2+(y-k)^2=r^2

(x+1)^2+(y-5/2)^2=36.24