1. Equations of Circles Advanced Geometry Conic Sections Lesson 1

2. An equation for a circle with center at (h, k) and radius of r units is

3. Example: Write an equation for each circle described. center at (-5, -3), r =

4. Example: Write an equation for each circle described. center at (3, -2), d = 10

5. Example: Write an equation for each circle described. center at the origin, r = 11

6. Example: Graph

7. Example: Graph

8. Example: A circle with center at (5, 4) has a radius with endpoint (-3, 4). Write an equation of the circle.

9. Example: A circle with a diameter of 14 has its center in the third quadrant. The lines y = 5 and x = 4 are tangent to the circle. Write an equation of the circle.

10. Example: A circle with a diameter of 10 has its center in the first quadrant. The lines y = -3 and x = -1 are tangent to the circle. Write an equation of the circle.

11. Example: Find the radius of a circle that has equation and contains (0, 2).

12. Example: The equation of a circle is Determine whether the line x = -1 is a secant, a tangent, or neither of the circle. Explain.

13. Example: The equation of a circle is Determine whether the line is a secant, a tangent, or neither of the circle. Explain.

14. Example: Strategically located substations are extremely important in the transmission and distribution of a power company’s electric supply. Suppose three substations are modeled by the points D(3, 6), E( -2, 1), and F(3, -4). Determine the location of a town equidistant from all three substations and write an equation for the circle.