Carilah persamaan lingkaran yang memenuhi persyaratan: a. Pusat (1,1), jari-jari 1 b. Pusat (-2,3), jari-jari 4 c. Pusat (2,-1), melalui (5,3) d. Diameter AB, d

jawab

a) (x -1)² +(y-1)² = 1
x² + y² - 2x - 2y  + 1= 0

b) (x +2)² + (y-3)² = 16
x² + y² + 4x  - 6y - 3 = 0

c) (x -2)² + (y+1)² = (5-2)² +(3+1)² = 25
x² + y² - 4x + 2y - 20 = 0

d) P = 1/2 (A + B)
a= 1/2(1+3) = 2
b = 1/2(3+7)= 5
(x- 2)² + (y - 5)² = (3-2)² + (7-5)² = 5
x² + y² - 4x - 10y +24 = 0

a. (h, k) = (1, 1)
r = 1

(x - h)² + (y - k)² = r²
(x - 1)² + (y - 1)² = 1²
(x - 1)² + (y - 1)² = 1

x² - 2x + 1 + y² + 2y + 1 - 1 = 0
x² + y² - 2x - 2y + 1 = 0

b. (h, k) = (-2, 3)
r = 4

(x - h)² + (y - k)² = r²
(x - (-2))² + (y - 3)² = 4²
(x + 2)² + (y - 3)² = 16

x² - 4x + 4 + y² + 6y + 9 - 16 = 0
x² + y² + 4x - 6y - 3 = 0

c. (h, k) = (2, -1)
melalui (5,3)

(x - 2)² + (y - (-1))² = (5 - 2)² +(3 + 1)² = 25
(x - 2)² + (y + 1)² = (5 - 2)² + (3 + 1)² = 25

x² - 4x + 4 + y² + 2y - 1 - 25 = 0
x² + y² - 4x + 2y - 20 = 0

d) P = 1/2 (A + B)
a= 1/2(1+3) = 2
b = 1/2(3+7)= 5
(x- 2)² + (y - 5)² = (3-2)² + (7-5)² = 5
x² + y² - 4x - 10y +24 = 0

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