1、 1 1,4,5 7 2,3,6 1.(2015 ) C:+=1(ab0) ,M C , M C F -1. (1) C ; (2) A,B C , M A,B , F MB AM P, : P . (1) : a-c= -1, = = . a= ,c=1, C +y 2 =1. (2) : M(x0,y0)(y0 0), + =1, AM y= (x+ ), FP MB, FP y=- (x-1), x+ =- (x-1), + =1, - =2, x=2+ , P x=2+ . 2.(2016 ) P F(1,0) x=2 , P 2 E, F x E A,B , l:y=mx+n E C
2、,D , AB ( A,B ). (1) E ; (2) l x 2 +y 2 =1 , ACBD . , l ; , . :(1) P(x,y), = , +y 2 =1. E +y 2 =1. (2) C(x1,y1),D(x2,y2), |AB|= . m=0 , . m 0 , l x 2 +y 2 =1 , =1, m 2 +1=n 2 . y (m 2 +)x 2 +2mnx+n 2 -1=0, =4m 2 n 2 -4(m 2 +)(n 2 -1)=2m 2 0, x1= ,x2= , S ACBD=|AB|x2-x1|= = , 2|m|= , m= , n= , , l y=
3、 x- y=- x+ ACBD , . 3.(2016 ) A M:x 2 +5y 2 =5 y ,F M , F l M B,C . (1) |OB|=|OC|, B,C ; (2) l, |AB|=|AC|? , l , , . :(1) x 2 +5y 2 =5 +y 2 =1, 3 c=2, F(2,0),A(0,1). , |OB|=|OC| l : l x , x=2,y= . B,C (2, ) (2,- ). l x ,B,C ( ,0) (- ,0). (2) , l x ,|AB|=|AC|, l y=0. l x , l . l , F k, l M B(x1,y1),C
4、(x2,y2),BC N(x0,y0), l:y=k(x-2). (1+5k 2 )x 2 -20k 2 x+20k 2 -5=0, x1+x2= . x0= ,y0= , |AB|=|AC|, AN BC. k=-1, 5k 2 -8k+1=0, k= , l y= (x-2). , l y=0 y= (x-2). 4.(2015 ) C , x , e= , 2. 4 (1) C ; (2) l:y=kx+m C A,B (A,B ), AB C D, : l , . (1) : -=1(a0,b0), = ,2b=2, a 2 +b 2 =c 2 , a=2,b=1, -y 2 =1.
5、(2) : A(x1,y1),B(x2,y2), (1-4k 2 )x 2 -8mkx-4(m 2 +1)=0, x1+x2= ,x1x2= , y1y2=(kx1+m)(kx2+m)=k 2 x1x2+mk(x1+x2)+m 2 = . AB C D(-2,0), kADkBD=-1, =-1, y1y2+x1x2+2(x1+x2)+4=0, + + +4=0, 3m 2 -16mk+20k 2 =0. m=2k m= . m=2k ,l y=k(x+2), (-2,0), ; m= ,l y=k(x+ ), (- ,0), . l , (- ,0). 5.(2016 ) C:x 2 =4y
6、. (1) P l:x-y-2=0 , P C PA,PB, P(x0,y0) l , AB ; (2) P l , |AF| |BF| . :(1) C x 2 =4y, y=x 2 , y =x. 5 A(x1,y1),B(x2,y2)( y1=,y2=), PA,PB x1,x2, PA y-y1=(x-x1), y=x-+y1, x1x-2y-2y1=0. PB x2x-2y-2y2=0. PA,PB P(x0,y0), x1x0-2y0-2y1=0, x2x0-2y0-2y2=0, (x1,y1),(x2,y2) x0x-2y0-2y=0 . AB x0x-2y-2y0=0. (2)
7、 |AF|=y1+1,|BF|=y2+1. |AF| |BF|=(y1+1)(y2+1)=y1y2+(y1+y2)+1, x y 2 +(2y0- )y+ =0, y1+y2= -2y0,y1y2= , |AF| |BF|=y1y2+(y1+y2)+1= + -2y0+1. P(x0,y0) l , x0=y0+2, + -2y0+1=2 +2y0+5=2(y0+) 2 +, y0=- ,|AF| |BF| , . 6.(2015 ) C:+=1(ab0) (1, ), . (1) C ; (2) y=k(x-1)(k 0) C A,B , M C , AM BM y P,Q, PQ x ?
8、, ; , . :(1) a=2,b=1. C +y 2 =1. (2) PQ x , (1+4k 2 )x 2 -8k 2 x+4k 2 -4=0, A(x1,y1),B(x2,y2), 6 x1+x2= ,x1x2= . M C , M(2,0), AM y= (x-2), P(0,- ). BM y= (x-2), Q(0,- ). PQ x N(x0,0), =0 , =(x0, ), =(x0, ), = + = + =0 , (x1-2)(x2-2)=x1x2-2(x1+x2)+4= -2 +4= , y1y2=k(x1-1) k(x2-1)=k 2 x1x2-(x1+x2)+1=
9、k 2 ( - +1)= , + = + = -3=0, x0= . x ( ,0) (- ,0). PQ x ( ,0). 7.(2016 ) C:+=1(ab0) F1,F2, , F1 l C M,N , MNF2 8. (1) C ; 7 (2) O C A,B , : O AB , . :(1) 4a=8, a=2. e=, = =1-e 2 =, b 2 =3. C +=1. (2) , AB , A(x0,x0),B(x0,-x0). A,B C , +=1, = , O AB d= = . AB , AB y=kx+m. y (3+4k 2 )x 2 +8kmx+4m 2 -12=0, 0 3+4k 2 m 2 . A(x1,y1),B(x2,y2), y1=kx1+m,y2=kx2+m, x1+x2=- ,x1x2= . OA OB, x1x2+y1y2=0, x1x2+(kx1+m)(kx2+m)=0, (k 2 +1)x1x2+km(x1+x2)+m 2 =0. (k 2 +1) - +m 2 =0, 7m 2 =12(k 2 +1), 0. O AB d= = = . , O AB , .
