1. tentukan persamaan garis singgung pada lingkaran L = (x+2)² + (y-1)² =25 di titk (-6,4) 2. Carilah Persamaan Garis Singgung pada lingkaran L = x² + y² = 25 y

Persamaan garis singgung pada lingkaran
1. (x+2)^2 + (y-1)^2 = 25 di (6,4)
(-6+2)(x+2) + (4-1)(y-1)^2 = 25
-4(x+2) + 3(y-1) = 25
-4x-8 + 3y -3 = 25
-4x  + 3y = 36
4x - 3y = - 36

2. x^2+ y^2 = 50 di (7,-1)
7(x-0)² + -1(y-0)= 50
7x - y = 50

3. (x+2)² +(y-3)² =  8  dgn m = -1
y- b = m(x-a) +- r √(m²+1)
y-3 = -1(x+2) +-√8 √2
y-3  = -x -2 +-√16
y= -x -2 + 3 + 4  atau y = -x -2 +3 - 4
y = -x + 5  atau y = -x - 3

4. (x-1)² +(y-4)² = 25 ditik (x1,y1)= (-3, 1)
(x1-1)(x-1) +(y1-4)(y-4) = 25
(-3-1)(x-1) +(1-4)(y-4) = 25
-4(x-1)  -3(y-4) = 25
-4x + 4 -3y +12 = 25
-4x - 3y = 9
4x + 3y = -9

5. titik singgung (2,4)
r jarak  (2,4) ke garis x+y = 3

| r| = (2+4-3)/ √(1²+1²)
|r| = 3/√2 = 3/2 √2
r² = (3/2 √2)² = 9/2

pusat (a,b) 
r = jaak (a,b) ke ttik (2,4)
r² = (a-2)² +(b-4)² = 9/2 ...(1)

pusat (a,b) pada garis x+y = 3
a + b = 3
a= 3 - b ....(2)
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(2) sub (1)
{ 3-b - 2)² + (b-4)² = 9/2
(1-b)² + (b-4)² = 9/2
2(1-2b+b²) + 2(b²-8b+16) = 9
2 - 4b + 2b² + 2b²-16b +32 -9 = 0
4b² -20b -25 =0
(2b - 5)^2 -0
b = 5/2
a = 3 - b = 3 - 5/2 = 1/2
Pers ling (x-a)² +(y-b)² = r²
(x - 1/2)² + (y- 5/2)² = 9/2