1、 1 2 1 2,3 4 1.(2016 ) xOy , O ,x , P (4 ,), C 2 +4 sin =4. (1) P C ; (2) Q C , PQ M l: (t ) . :(1) P (4 ,), x= cos =6,y= sin =2 , P (6,2 ). 2 +4 sin =4, x 2 +y 2 +4 y=4, x 2 +(y+2 ) 2 =16, C x 2 +(y+2 ) 2 =16. (2) l: (t ) l x-y-5=0, C x 2 +(y+2 ) 2 =16, Q(4cos ,4sin -2 ), M (2cos +3,2sin ), M l d=
2、= . 2 cos ( +)=-1 , d 2+ , M l 2+ . 2.(2016 ) xOy , , x , , l (t ), C =1. (1) l C ; (2) , C C , M(x,y) C , 4x 2 +xy+y 2 , M . :(1) l (t ) x-y- =0, C =1 x 2 +y 2 =1. (0,0) l d= =1, r, l C 1. (2) C (0 0,sin cos 0. 0, ), (0, ), t1+t2=-4(sin +cos ),t1t2=4. t10,t20. |PM|+|PN|=|t1|+|t2|=|t1+t2|=4(sin +cos
3、 )=4 sin ( +), (0, ) ( +) (, ), sin( +) 1, |PM|+|PN| (4,4 . 4.(2016 ) C1 (t ), t=1 , C1 A, t=-1 , C1 B. O , x , C2 = . (1) A,B ; (2) M C2 , |MA| 2 +|MB| 2 . :(1) t=1 , A(-1, ), = =2,tan = =- , = , A (2, ). t=-1 , B(1,- ), 4 B (2, ). (2) = , 2 (4+5sin 2 )=36, 4 2 +5( sin ) 2 =36, 4(x 2 +y 2 )+5y 2 =36, +=1, C2 M(3cos ,2sin ), |MA| 2 +|MB| 2 =(3cos +1) 2 +(2sin - ) 2 +(3cos -1) 2 +(2sin + ) 2 =18cos 2 +8sin 2 +8=10cos 2 +16 26, cos = 1 , 26. |MA| 2 +|MB| 2 26.
