Question

1.Tentukan persamaan garis singgung lingkaran di titik-titik berikut ini.a.x2 + y2 = 9 di titik (2, –5)c.x2 + y2 = 4 di titik (–4, –7)b.x2 + y2 = 16 di titik (–3, 4)d.x2 + y2 = 12 di titik (5, 6)
2.Tentukan persamaan garis singgung lingkaran di titik-titik berikut ini.a.(x – 4)2 + (y + 3)2 = 36 di titik (–2, 1)b.(x + 2)2 + (y – 3)2 = 9 di titik (–2, 6)c.(x – 1)2 + (y + 5)2 = 7 di titik (3, –2)d.(x + 5)2 + (y – 2)2 = 10 di titik (4, 3)

Answer 1

1. a= X1.x +y1.y=r²
2.x+-5.y=9
2x-5y=9
1b. x1.x+y1.y=r²
-3.x+4.y=16
-3x.4y=16
1c. x1.x+y1.y=r²
-4.x+-7.y=4
-4x-7y=4
1d. x1.x+y1.y=r²
5.x+6.y=12
5x+6y=12

2a. (x1-a)(x-a)+(y1-b)(y-b)=r²
(-2-4)(x-4)+(1+3)(y+3)=36
-6.(x-4)+4.(y+3)=36
-6x+24+4y+12=36
-6x+4y+36=36
2b. (x1-a)(x-a)+(y1-b)(y-b)=r²
(-2+2)(x+2)+(6-3)(y-3)=r²
0.(x+2)+3(y-3)=9
0+3y-9=9
3y-9=9
2c. (x1-a)(x-a)+(y1-b)(y-b)=r²
(3-1)(x-1)+(-2+5)(y+5)=7
2(x-1)+3(y+5)=7
2x-2+3y+15=7
2x+3y+13=7
2d. (x1-a)(x-a)+(y1-b)(y-b)=r²
(4+5)(x+5)+(3-2)(y-2)=10
9(x+5)+1(y-2)=10
9x+45+y-2=10
9x+y+43=10