Today, we will understand equations of circles and graphing a circle in the coordinate plane
And
By the end of class today, you will be able to find the center of a circle and its radius from the equation of that
circle.
Notes
Writing and Graphing Equations of Circles
Circles centered at the origin –
Example 1
Write the equation of the circle shown.
Circles centered at (h, k) –
Example 2
Write the standard equation of a circle with center (0, –9) and radius 4.2.
More Examples
Write the standard equation of a circle with the given center and radius.
3. Center (0, 0), radius 2.5
4. Center (–2, 5), radius 7
What if we have the center and a point on the circle???
5. The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle.
Even more examples!!!
6. The point (3, 4) is on a circle whose center is (1, 4). Write the standard equation of the circle.
7. The point (–1, 2) is on a circle whose center is (2, 6). Write the standard equation of the circle.
Graphing examples
8. The equation of a circle is (x – 4)2 + (y + 2)2 = 36. Graph the circle.
9. The equation of a circle is (x – 4)2 + (y + 3)2 = 16. Graph the circle.
10. The equation of a circle is (x + 2)2 + (y – 1)2 = 25. Graph the circle.