1. Warm-Up Find the distance and the midpoint. 1. (0, 3) and (3, 4)

2. Graph and Write Equations of Circles
Section 9-3
Graph and Write Equations of Circles

3. Vocabulary
Circle – The set of all points (x, y) in a plane that are equidistant from a fixed point.
Center – The fixed point of a circle.
Radius – The distance r between the center and any point (x, y) on the circle.

4. Standard Equation of a Circle with Center at the Origin
x2 + y2 = r2

5. Example 1 x2 + y2 = 4 Center : (0, 0) Radius: √4 = 2
Graph x2 – 4 = – y2. Identify the radius of the circle.
Step 1: Rewrite the equation in standard form.
x2 + y2 = 4
Center : (0, 0)
Radius: √4
= 2
Step 2: Identify the center and radius.
Step 3: Draw the circle.

6. Example 2 d = √(x2 – x1)2 + (y2 – y1)2 d = √(-4 – 0)2 + (7 – 0)2
The point (-4, 7) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.
Step 1: Use the distance formula.
Because the point (-4, 7) lies on the circle, the circle’s radius r must be the distance between the center (o, 0) and (-4, 7).
Step 2: Write the equation of the circle.
d = √(x2 – x1)2 + (y2 – y1)2
d = √(-4 – 0)2 + (7 – 0)2
d = √(-4)2 + (7)2
x2 + y2 = 65
d = √ 65

7. Example 3 m = -6 – 0 5 – 0 m = 5 6 = -6 5 y – y1 = m(x – x1)
What is an equation of the line tangent to the circle x2 + y2 = 61 at (5, -6)?
Step 1: Find the slope of the line.
A line tangent to a circle is perpendicular to the radius at the point of tangency.
Step 2: Find the slope of the tangent line.
m = -6 – 0
5 – 0
m = 5 6
= -6 5
Step 3: Use point-slope form to find the equation.
y – y1 = m(x – x1)
y – (-6) = 5(x – 5) 6
y = 5x – 61
y + 6 = 5x – 25

8. Homework Section 9-3 Pages 629 –630 1, 3 – 8, 10 – 12, 17,
18, 22, 23, 26, 28, 31,
32, 34, 44, 45,
46, 55, 58, 62