1. Warm Up Find the slope of the line that connects each pair of points. –1 1 6 1. (5, 7) and (–1, 6) 2. (3, –4) and (–4, 3)

2. Warm Up Find the distance between each pair of points. 173. (–2, 12) and (6, –3) 4. (1, 5) and (4, 1) 5

3. LESSON 11.2 CIRCLES AND POINTS OF INTERSECTION LO: How to write an equation of a circle and sketch its graph

4. A circle is the set of points in a plane that are a fixed distance, called the radius, from a fixed point, called the center. Because all of the points on a circle are the same distance from the center of the circle, you can use the Distance Formula to find the equation of a circle.

5. Write the equation of a circle with center (–3, 4) and radius r = 6. Example 1: Using the Distance Formula to Write the Equation of a Circle Use the Distance Formula with (x 2, y 2 ) = (x, y), (x 1, y 1 ) = (–3, 4), and distance equal to the radius, 6. Use the Distance Formula. Substitute. Square both sides.

6. Write the equation of a circle with center (4, 2) and radius r = 7. Use the Distance Formula with (x 2, y 2 ) = (x, y), (x 1, y 1 ) = (4, 2), and distance equal to the radius, 7. Use the Distance Formula. Substitute. Square both sides. Example 2

7. Notice that r 2 and the center are visible in the equation of a circle. This leads to a general formula for a circle with center (h, k) and radius r.

8. If the center of the circle is at the origin, the equation simplifies to x 2 + y 2 = r 2. Helpful Hint

9. Write the equation of the circle. Example 3: Writing the Equation of a Circle (x – 0) 2 + (y – 6) 2 = 1 2 x 2 + (y – 6) 2 = 1 the circle with center (0, 6) and radius r = 1 (x – h) 2 + (y – k) 2 = r 2 Equation of a circle Substitute.

10. Use the Distance Formula to find the radius. Substitute the values into the equation of a circle. (x + 4) 2 + (y – 11) 2 = 225 the circle with center (–4, 11) and containing the point (5, –1) (x + 4) 2 + (y – 11) 2 = 15 2 Write the equation of the circle. Example 4: Writing the Equation of a Circle

11. Use the Distance Formula to find the radius. Substitute the values into the equation of a circle. (x + 3) 2 + (y – 5) 2 = 169 Find the equation of the circle with center (–3, 5) and containing the point (9, 10). (x + 3) 2 + (y – 5) 2 = 13 2 Example 5

12. A point of intersection of two graphs is a point that lies on both graphs. Two graphs can have no point of intersection, one point, or two or more points.

14. Example 7 Find the points of intersection of the graphs of the following equations.

15. Homework Pg. 579 # 5 – 37 odd