DRILLDRILL• Find the area and circumference of each

circle in terms of (pi) with the given information for each circle.

A) Radius = 5 in.B) Diameter = 14 ft. C) Radius = ½ yd.D) Radius = 3x & Diameter = 2x + 20

12.112.1Circles in The Coordinate PlaneCircles in The Coordinate Plane

X & Y InterceptsX & Y Intercepts

• X – Intercept: is where the graph crosses the x-axis and the value of y = 0.

• Y-Intercept: is where the graph crosses the y-axis and the value of x = 0.

Ex: x2 + y2 = 36

Ex: (x + 2) 2 + (y – 1) 2 = 16

Deriving the Equation of a CircleDeriving the Equation of a Circle

Equation of a Circle

The center of a circle is given by (h, k)

The radius of a circle is given by r

The equation of a circle in standard form is (x – h)2 + (y – k)2 = r2

Finding the Equation of a Circle

Circle A

The center is (16, 10)

The radius is 10

The equation is (x – 16)2 + (y – 10)2 = 100

Finding the Equation of a Circle

Circle B

The center is (4, 20)

The radius is 10

The equation is (x – 4)2 + (y – 20)2 = 100

Finding the Equation of a Circle

Circle O

The center is (0, 0)

The radius is 12

The equation is x 2 + y 2 = 144

Graphing Circles

(x – 3)2 + (y – 2)2 = 9

Center (3, 2)

Radius of 3

Graphing Circles

(x + 4)2 + (y – 1)2 = 25

Center (-4, 1)

Radius of 5

Graphing Circles

(x – 5)2 + y2 = 36

Center (5, 0)

Radius of 6

Writing Equations of Circles

Write the standard equation of the circle:

Center (4, 7) Radius of 5

(x – 4)2 + (y – 7)2 = 25

Writing Equations of Circles

Write the standard equation of the circle:

Center (-3, 8) Radius of 6

(x + 3)2 + (y – 8)2 = 36

Writing Equations of Circles

Write the standard equation of the circle:

Center (2, -9) Radius of

(x – 2)2 + (y + 9)2 = 11

11

Writing Equations of Circles

Write the standard equation of the circle:

Center (0, 6) Radius of

x 2 + (y – 6)2 = 7

7

Writing Equations of Circles

Write the standard equation of the circle:

Center (-1.9, 8.7) Radius of 3

(x + 1.9)2 + (y – 8.7)2 = 9

HomeworkHomework• Complete the Worksheet