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

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

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

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.

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.

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

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.

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

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.

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

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

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.

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

Homework Pg. 579 # 5 – 37 odd