1. Warm Up May 14th
Find the area and circumference of a circle with a diameter of 9 in.
Find the area of a circle is the circumference is 41 ft.
Find the perimeter and area of the shape.
6 yd
4 yd

2. Homework Questions??

3. Equations of Circles
Definition: A circle is the set of all points in a plane at a distance “ r ” (radius) from a given point called the center.
If the circle has its center at the origin, the equation is of the form x2 + y2 = r2

4. Radius of a Circle
x2 + y2 = 25 is a circle with a center at ( , ) and a radius of ______.
To change the size of the circle, just change r.
Write the equation of a circle with a center at the origin that has a radius of 7.

5. Center of a Circle
If we want to change the center, we have to change the equation.
The standard form for the equation of a circle not centered at the origin is (x – h)2 + (y – k)2 = r2
where (h, k) is the center and r is the radius of the circle.

6. Equations of a Circle
Write an equation of the circle in standard form.
Center Radius Equation
(2, 3) 5
(6, -2) -13
(-4, -9) 2.5

7. Equations of a Circle
BE CAREFUL! Make sure you read/understand the information given to you.
Write an equation of a circle with diameter of 24, centered at (4, -3).

8. Graphing a Circle
Graph a circle with a center at (4, 2) and a radius of 3

9. Graphing a Circle (x + 2)2 + (y – 3)2 = 16
Graph this circle after finding its radius and center:
(x + 2)2 + (y – 3)2 = 16
Center: __________
Radius: __________

10. Equations from a Graph Write the equation for the circle shown below.
Find the circumference & area.

11. Equations from a Graph Write the equation for the circle shown below.
Find the circumference & area.

12. Using Distance & Midpoint w/ Circles
Recall the distance between two points can be found using the distance formula:
Write the equation of a circle that passes through (3, -4) and has a center at the origin.

13. Using Distance to Find Radius
Write the equation of a circle that passes through (1, 9) and has a center at (6, 7).

14. Using Distance to Find Radius
Write the equation of a circle that passes through (-6, 20) and has a center at (2, 5).

15. Using Midpoint to Find Center
Write the equation of a circle with a diameter that goes from (0, 0) to (10, 24)
Center?
Midpoint Formula
Radius?
Distance Formula
Equation: ___________________