1. 11.0 Analytic Geometry & Circles
Objectives:
Define and identify a conic section.
Define analytic geometry.
Define a circle.
Write the equation of a circle.
Identify important characteristics of circles.
Graph circles.

2. Conic Sections Conic Sections –
The geometric figures formed by slicing a right circular double-napped cone at different angles with a plane.
Analytic Geometry –
The study of geometric properties of objects using the coordinate system.

3. Circles
A circle is a special type of ellipse where all the points in it are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius.
The Standard Form for the equation of a circle:

4. Circles
By centering the circle at the origin we obtain:

5. Example #1
Graph and describe the circle whose equation is:

6. Example #1
Graph the circle with center (1, -3) and radius 4, and find its equation.

7. Example #2
Graph the circle with center (4, -2) that passes through (3,5), and find its equation.

8. Example #3
Write the equation of the circle into standard form and graph.

9. Example #3
Write the equation of the circle into standard form and graph.

10. Example #3
Write the equation of the circle into standard form and graph.

11. Example #3
Write the equation of the circle into standard form and graph.

12. Example #4
Find the equation of a circle tangent to the y-axis (meaning it touches in a single point) that is centered at (5, -1).
Since it is tangent to the y-axis, the radius is 5.

13. Example #5
Find the equation of a circle whose endpoints of the diameter are (4, -6) & (-1, -2).
Since the endpoints of the diameter are given, the center can be found by using the midpoint formula. The radius is then half the distance between the two endpoints.