Download 11.1-2 Notes: Circles in the Coordinate Plane

 11.1‐2 Notes: Circles in the Coordinate Plane Name_________________ Objective: Equation of a Circle Theorem The standard form of an equation of the circle with center (h, k) and radius r is: Example 1: State the center and the radius of each equation of a circle below: a) (x – 4)2 + (y + 3)2 = 4 b) x2 + (y – 5)2 = 36 c) 2(x – 4)2 + 2y2 = 200 Example 2: Write the standard equation of the circle with center (5, ‐2) and radius 7. Example 3: Write the standard equation of each circle. a. center (3, 5); radius 6 b. center (‐2, ‐1); radius 2 If you know the center of the circle and a point on the circle, you can write the standard equation of the circle. Example 4: Write the standard equation of the circle with center (1, ‐3) that passes through the point (2, 2). Example 5: Write the standard equation of the circle with center (2, 3) that passes through the point (‐1, 1). If you know the standard equation of a circle, you can describe the circle by naming its center and radius. Then you can use this information to graph the circle! Example 6: Find the center and the radius of the circle with equation (x – 3)2 + (y + 2)2 = 9. Then graph the circle. Example 7: Write the equation of the circle shown. Sometimes you will need to put an equation into standard form by completing the square. Once the equation is in standard form, find the center point and radius. Example 8: Put each equation into standard form, then graph using the center and radius a. x 2 y 2 4 x 6 y 12 0 x 2 y 2 4 x - 8 y 11 0 b.