Question

Bantu dong no 1-3 bagian B. berikut penjelasannya ya

Answer 1

1.
A(0,1) dan B(4,5) --> AB diameter
P(a,b) --> a = 1/2 (0+4) = 2,  dan b = 1/2 (1+5) = 3
P(a,b) = (P(2,3)

r = 1/2 (AB) = 1/2 √(4-0)²+(5-1)²= 1/2 √32
r = 2√2 --> r² = 8
Pers ling P(2,3) dgn r² = 8 --> (x-2)² + (y-3)² = 8
pers garis singung di A(0,1) --> x1 = 0 , y1 = 1
(x1-2)(x-2) +(y1-3)(y-3) = 8
-2(x-2) + (1-3)(y-3) = 8
-2(x-2) - 2(y-3) = 8
-2x + 4 + -2y + 6 - 8 = 0
-2x -2y + 2= 0
x + y + 1 = 0

2. garis singgung di A(12,5) pada ling x² +y² = 169 adalah :
12(x-0) + 5(y-0) = 169 atau 12x + 5y =169
.
garis 12x + 5y = 169 menyinggung ling (x-5)²+(y-12)² = p
p = r²
r = jarak pusat (5, 12)  ke garis 12x + 5y = 169
|r| = {12(5) +5(12) - 169}/ (√(12²+5²)
|r|= (-49/13) = 49/13
p = r² = (49/13)² = (2.401 / 169)

 
3.
a) r lingkaran = k , menyinggung sb y di (0,3) --> Pusat (k, 3) dgn r = k
(x-k)² + (y-3)² =  k²

b) lingkaran melalui (x,y) = (2,7) sub ke ling --> (2-k)² + (7-3)² = k²
(2-k)² - (k)² = -16
(2-k+k)(2-k-k)  = -16
2(2-2k) = -16
2(-2)(-1+k) = -16
-1+k = 4
k = 5
k = 5 sub ke Pers lingkaran (x-k)² +(y-3)² = k² --> (x-5)² +(y-3)² = 25

panjang tali busur yg terptong sub x --> y = 0
(x-5)² +(0-3)² = 25
(x-5)² = 25-9 = 16
x - 5 = 4  atau x - 5 = - 4
x = 9 atau x = 1
panjang talibusur = (9-1) satuan = 8 satuan