Circles And Circular Functions Worksheet - Dr. Neal, Math 116

Circles And Circular Functions Worksheet - Dr. Neal, Math 116 - 2008 Page 3

Dr. Neal, Fall 2008

General Equation of a Circle

The equation of the circle with center (h , k ) and radius of length r is given by

(x − h)

+ (y − k )

= r

Example 3. (a) Give the equation of the circle having center (4, –6) and radius 9.

(b) Graph the circle by plotting the center and the 4 “directional” points on the circle.

the circle and state the domain and range for each.

Solution. Center: (4, –6) and r = 9 → (a) Equation: (x − 4)

+ (y + 6)

= 81

(b) To find the four “directional” points, go to the center (4, –6) then add ± 9 to the x -

coordinate to obtain the points (–5, 6) and (13, 6). Then go back to the center (4, –6) and

add ± 9 to the y -coordinate to obtain the points (4, 3) and (4, –15).

(4, 3)

(–5, –6)

(4, –6)

(13, –6)

r = 9

(4, –15)

(x − 4)

+ (y + 6)

= 81 → (y + 6)

= 81− (x − 4)

→ y + 6 = ± 81− (x − 4)

→ y = ± 81 − (x − 4)

− 6

Upper Semi-Circle Function

Lower Semi-Circle Function

y = 81− (x − 4)

− 6

y = − 81 − (x − 4)

− 6

Domain: −5 ≤ x ≤ 13

Range: −6 ≤ y ≤ 3

Domain: −5 ≤ x ≤ 13 Range: −15 ≤ y ≤ − 6

Circles And Circular Functions Worksheet - Dr. Neal, Math 116 - 2008 Page 3