Equations of Circles
Equation of a Circle Standard Equation of a Circle: An equation of a circle with center (h, k) and radius r is (x – h)2 + (y – k)2 = r2.
Finding the Center and the Radius when given the equation Center (0, 0), r = 5 Center (0, 0), r = 10 Center (5, -4), r = 7 Center (-7, 3), r = Center (0, 1), r = Center (3, 0), r = 9
Writing the Equation of a Circle Center (0, 0) r = 2 Center (0, 1) r = 6 Center (-3, 5) r = 2.5 Center (-5, 10) r = 10 Center (8, 0) r = 1 Center (6, 9) r = 3.4 x2 + y2 = 4 x2 + (y – 1)2 = 36 (x + 3)2 + (y– 5)2= 6.25 (x + 5)2 + (y–10)2= 100 (x – 8)2 + y2= 1 (x– 6)2 + (y– 9)2= 11.56
Writing the Equation of a circle 2. A circle whose center is at (-3, 2) passes through (-7, 2). What is the length of the radius of the circle? Write the equation of the circle. Answers: a. r = 4 b. (x + 3)2 + (y - 2)2 = 16
Graphing a Circle Find the center and the radius and graph the circle. Answers: center (0, 0) radius = 3
Graphing a Circle Find the center and the radius and graph the circle. Answers: center (1, -2) radius = 5
Graphing a Circle Find the center and the radius and graph the circle. Answers: center (3, 0) radius = 2
Graphing a Circle Given Its Equation Graph the circle whose equation is (x + 4)2 + (y – 1)2 = 25.
Converting from General Form to Standard Move the x terms together and the y terms together. Move C to the other side. Complete the square (as needed) for x. Complete the square(as needed) for y. Factor the left & simplify the right.
WRITE and GRAPH A) write the equation of the circle in standard form x² + y² - 4x + 8y + 11 = 0 Group the x and y terms x² - 4x + y² + 8y + 11 = 0 Complete the square for x/y x² - 4x + 4 + y² + 8y + 16 = -11 + 4 + 16 (x – 2)² + (y + 4)² = 9 YAY! Standard Form! B) GRAPH Plot Center (2,-4) Radius = 3
WRITE and GRAPH A) write the equation of the circle in standard form 4x² + 4y² + 36y + 5 = 0 Group the x and y terms Complete the square for x/y 4x² + 4(y² + 9y) = -5 4x² + 4(y² + 9y + 81/4) = -5 + 81 4x² + 4(y + 9/2)² = 76 x² + (y + 9/2)² = 19 YAY! Standard Form! B) GRAPH Plot Center (0 , -9/2) Radius = √19 = 4.5
8. Write the standard equation of the circle. State the center & radius.
9. Write the standard equation of the circle. State the center & radius.
10. Write the standard equation of the circle 10. Write the standard equation of the circle. State the center & radius.
Example: Write the equation and find the center and radius length of : Group terms Complete the square
Write the equation and find the center and radius length of :