1. 28. Writing Equations of Circles

2. CONIC SECTIONS

3. (x, y) r y x
We find the equation of a circle from where the center is and the distance from the center to a point on the circle (the radius).

4. The equation is found using the Pythagorean Theorem
Center: (h, k) Radius: r

5. Find the radius and graph.
Circles
Center at the origin
Find the radius and graph.
x2 + y2 = 36
6x2 + 6y2 = 60

6. Center that is translated
Circles
Center that is translated
Find the center, radius and graph.
(x-2)2 + y2 = 16
Center: ________ r: ______
2(x+3)2 + 2(y+2)2 = 50
Center: ________ r: ______

7. Getting an equation into standard form
To write the standard equation of a translated circle, you will need to complete the square.

8. 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

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

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

11. Write the equation of a circle with the given radius and whose center is the origin.

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

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

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

15. 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: _____

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

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