2. Definition of a Circle
 All points on a circle are equidistant from the
center of the circle.
 The distance between the center and any
point on the circle is the radius.

3. Equation of a Circle
 Can be derived from the distance formula.
 Only for circles with center at (0, 0)!

4. Graphing Circles
1. Write in standard form.
2. Find the radius.
3. Plot four intercepts r units from the origin.
4. Connect with a circle.
Example:
Graph

5. Your Turn!
 Graph

6. Writing Equations
1. Use the distance formula to find r.
2. Plug it into standard form equation.
Example:
The point (1, 4) is on a circle centered at
(0,0). Write the equation of the circle.

7. Your Turn!
 The point (5, 1) is on a circle centered at
(0,0). Write the equation of the circle.

8. Tangent Lines
 A line is tangent to a circle if it touches the
circle at one point and is perpendicular to
the radius.

9.  To find the equation:
1. Find the slope of the radius through the
given point.
2. Find slope perpendicular to that (opp.
reciprocal)
3. Use point-slope form to write equation.

10. Example
 Write an equation of the line tangent to the
circle at (2, 3).

11. Your Turn!
 Write an equation of the line tangent to the
circle at (-2, 4).