Standard Equations of Circles

1. Standard Equations of Circles Lesson 9.1A R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles CGT.5.G.4 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

2. Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 h = x coordinate of the center k = y coordinate of the center r = radius

3. Example Write the equation for the circle with the given radius and center r = 7 Center @ (8, 12)

4. Example #2 Write the equation of the circle with the given center and radius r = √24 Center @ (0, 2)

5. Now You Try… Write the equation of a circle with the given radius and center r = 16 Center @ (-3, -6)

6. Example Write the standard equation of the given circle.

7. Now You Try… Write the equation of the given circle.

8. Example Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph: (x – 5)2 + (y – 8)2 = 4

9. Example #2 Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph: (x +3 )2 + (y – 7)2 = 8

10. Now You Try… Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph: x 2 + (y + 6)2 = 18