1. Writing Equations of Circles

2. CONIC SECTIONS

3. We will only look at Circles this year

4. The set of all points a given distance from a point (center)
Definition of a Circle
The set of all points a given distance from a point (center)

5. ( 𝑥 1 − 𝑥 2 ) 2 +( 𝑦 1 − 𝑦 2 ) 2 =𝑑

6. (x, y) r y x
𝑥 2 + 𝑦 2 = 𝑟 2

7. Find the radius and graph.
Circles
Center at the origin
Find the radius and graph.
(x+1)2 + (y-2)2 = 36

8. Find the radius and graph.
Circles
Center at the origin
Find the radius and graph.
(x-0)2 + (y-0)2 = 16

9. Center that is translated
Circles
Center that is translated
Find the center, radius and graph.
(x-2)2 + y2 = C: ____
r: _____
2(x+3)2 + 2(y+2)2 = 50

10. How is the equation of a circle similar to Pythagorean Theorem
Center: (h, k) Radius: r

11. Change: General → Standard
Write the Equation of the Circle in Standard Form.
Change: General → Standard
r = 4
Center (3, -2)

12. Getting an equation into standard form
To write the standard equation of a translated circle, you will need to complete the square.
Example:
Center: (4, 0) r: 3

13. Example!!!
Write the standard equation for the circle. State the center and radius.

14. Now we will work backwards and find the equation of a circle

15. Write the equation of a circle with the radius of 5 and whose center is the origin.

16. Example: Write the standard equation for the translated circle with center at (-2, 3)and a radius of

17. Another one
Write the equation of the circle with the center (3,-1) and the radius .
*Always look for Center: _______ and Radius: _____

18. Writing equations given a point
You must find the radius 1st using the distance formula

19. Write the equation of the circle with the point (4,5) on the circle and the origin as it’s center.
*Always look for Center: _______ and Radius: _____

20. Find equation of circle passing through (5, 1) with the center at (2,-3)

21. Another
Find equation of circle with diameter ending at points (5,3) and (-3, 13).

22. Verifying if a point lies on a circle
Last thing!
Verifying if a point lies on a circle
Plug the point into the equation of the circle and see if the resulting equation is true

23. Example