1. Writing equations for Circles

2. What are the 2 things you need to write an equation for a circle??
The Center: ( , )
The radius: r =

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

4. Writing equations: Example 5
Write the equation of the circle with the point (4,5) on the circle and the origin as it’s center.

5. Point (4,5) on the circle and the origin as it’s center.
*Always look for Center: _______ and Radius: _____

6. Practice!!
Write the equation of the circle with the point (-3,-5) on the circle and the origin as it’s center.
*Always look for Center: _______ and Radius: _____

7. Standard Equation of a Translated Circle
The standard equation for a circle with its center at (h, k) and a radius of r is:
This is different with both h and k. Both of the numbers are the opposite when plugged in.
Example:
Write the standard equation for the translated circle with center at (-2, 3)and a radius of 4.

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

9. Writing equations of circles
Find equation of circle passing through (2, 5) with the center at (0,0)
Find equation of circle passing through (-5, -5) with the center at (0,0)
Find equation of circle passing through (5, 1) with the center at (2,-3)
*Always look for Center: _______ and Radius: _____

10. You Try!!
(Try a picture to help!)
Find equation of circle passing through (-3, 4) with the center at (0,0)
Find equation of circle passing through (0,2) with the center at (-6,3)
Find equation of circle passing through (-2, -2) with the center at (-5,-8)
*Always look for Center: _______ and Radius: _____

11. Find an equation of a line tangent to a circle
Last thing!!
Find an equation of a line tangent to a circle
Find an equation of a line tangent to the circle
at (-1, 3)
The tangent line is perpendicular to the line from the origin to the point.
You’ll have slope and a point. Write the equation.

12. You Try!! Find an equation of a line tangent to the circle at (4, -1)
Find the slope from the center to the point (rise over run)
Find the Perpendicular slope (opposite reciprocal)
Write an equation with your NEW slope and point given y = mx+b or y – y1 = m(x – x1)

13. Practice WS Front and Back!
Circle Practice!!
Practice WS
Front and Back!