Tolong bantu jawab! titik P pusat lingkaran L , terletak pada garis AB dan AP : PB =2 : 1. jika A (1,9) , B (4,3) dan lingkaran melalui titik A maka jari-jari l

jawab

A(1,9)
B(4,3)

AP : PB = 2 : 1
1(AP) = 2(PB)
p - a = 2(b -p)
p - a = 2b - 2p
p + 2p = a + 2b
3p = a + 2b
p = 1/3 (a + 2b)

xp = 1/3 (ax + 2 bx) = 1/3 (1  + 2(4))= 1/3 (9) = 3
yp = 1/3 (ay + 2 by) = 1/3 (9 + 2(3)) = 1/3 (15) = 5
titik P (a,b) = (3, 5)

r = jarakAP
r² = (1-3)² +(9-5)² = 2² + 4²
r² = 20

pers lilngkaran  ( x- a)² + (y-b)² = r²
(x - 3)² +(y- 5)² = 20
atau
x² + y² -6x -10y + 9+25- 20 =0
x² + y² -6x -10y + 14 = 0