2. Definition of a Circle
ď‚— All points on a circle are equidistant from the
center of the circle.
ď‚— The distance between the center and any
point on the circle is the radius.
3. Equation of a Circle
ď‚— Can be derived from the distance formula.
ď‚— 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
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!
ď‚— The point (5, 1) is on a circle centered at
(0,0). Write the equation of the circle.
8. Tangent Lines
ď‚— A line is tangent to a circle if it touches the
circle at one point and is perpendicular to
the radius.
9. ď‚— 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.