1、 1 7 1,2,7,10,13,14,15 4,5,6,9,12 3,8,11 ( :30 ) 1. y=x+3 -=1 ( A ) (A)1 (B)2 (C)1 2 (D)0 : y=x+3 y=x , 1 . 2. C + =1(m0), y= x M x F, m ( B ) (A)2 (B)2 (C)8 (D)2 : c= , ( , ) + =1(m0) , + =1, m=2 . 3. C:-=1(a0,b0), d=(1,1) C A,B, AB (4,1), C ( B ) (A)2x y=0 (B)x 2y=0 (C) x y=0 (D)x y=0 : d=(1,1) y=
2、x+m, y (b 2 -a 2 )x 2 -2a 2 mx-a 2 m 2 -a 2 b 2 =0, A(x1,y1),B(x2,y2), AB (4,1). x1+x2= =8, y1+y2=8+2m=2, m=-3, 2 =8, a=2b, y= x. 4.(2016 ) 1 l +y 2 =1 A,B , |AB| ( C ) (A)2 (B) (C) (D) : l y=x+t, +y 2 =1, y x 2 +2tx+t 2 -1=0, =(2t) 2 -5(t 2 -1)0 t 2 0), MN y- =k(x-2), kx-y-2k+ =0, MN x 2 +y 2 =1 ,
3、MN 1, =1 k= k=- ( ), MN x-y- =0, x 2 +y 2 =1 N (,- ), |NF|= = . 7.(2015 ) y 2 =8x F C:-=1(a0,b0) , P y 2 =8x ,P C F1(0,c) x=-2 3, . : , y 2 =8x F(2,0), C:-=1(a0,b0) ax-by=0, = , a=2b. P C F1(0,c) x=-2 3, |FF1|=3, c 2 +4=9, c= , c 2 =a 2 +b 2 ,a=2b, a=2,b=1. -x 2 =1. :-x 2 =1 8.(2014 ) M(1,1) - C:+=1
4、(ab0) A,B , M AB , C . : A(x1,y1),B(x2,y2), 4 + =0, x1+x2=2 1=2,y1+y2=2 1=2, =-, + (-)=0, a 2 =2b 2 , a 2 =2(a 2 -c 2 ), a 2 =2c 2 = , e= . : 9. x 2 =8y F, l,P ,PA l,A , AF 60 , |PF| . : APF ,|PA|=|PF|,|AF|sin 60 =4, |AF|= , PAF= PFA=30 , P PB AF B, |PF|= =. : 10.(2016 ) C , x , 2, . (1) C ; (2) l M
5、(0,1), C A,B , =2 , l . :(1) +=1(ab0), c=1,=, a=2,b= , C +=1. (2) l , l y=kx+1, (3+4k 2 )x 2 +8kx-8=0, 0. A(x1,y1),B(x2,y2), =2 , x1=-2x2, 5 x2 ( ) 2 = , k 2 =,k= , l y= x+1, x-2y+2=0 x+2y-2=0. 11.(2016 ) C F1(-2,0),F2(2,0), C P F1,F2 2. (1) C ; (2) M(2,1) l C A,B , M AB , l ; (3) G(1,2), D C , |DF1
6、|+|DG| . :(1) , C a=1, c=2, b= = . x , C x 2 -=1. (2) A,B (x1,y1),(x2,y2), , 3(x1-x2)(x1+x2)-(y1-y2)(y1+y2)=0. M(2,1) AB , 12(x1-x2)-2(y1-y2)=0, kAB= =6. AB l y-1=6(x-2), 6x-y-11=0. (3) , |DF1|-|DF2|=2, |DF1|=|DF2|+2, |DF1|+|DG|=|DF2|+|DG|+2 |GF2|+2, G,D,F2 . |GF2|= = , |DF2|+|DG|+2 |GF2|+2= +2. |DF
7、1|+|DG| +2. 6 ( :15 ) 12.(2016 ) y 2 =2px(p0) F l B,C ,l A, |AF|=6, =2 , |BC| ( A ) (A) (B)6 (C) (D)8 : l , 00, b-. M(x1,y1),N(x2,y2), x1+x2=-1, =- +b=+b, (-,+b) y=x+3 , +b=-+3, b=2, :(-2,4),(1,1) 14.(2015 ) A(- ,0), B( ,0), P |PA|-|PB|=2, P y=k(x-2) k . : P 2a=2,c= , b= =1, P x 2 -y 2 =1(x0), y=x.
8、P y=k(x-2) 7 , k (- ,-1) (1,+ ). :(- ,-1) (1,+ ) 15. C:+y 2 =1(a0) x , A,B. , A,B C1,C2 P( O ), BP A. (1) C ; (2) OP l C M,N , OMN l . :(1) A(a,0),B(0,1), A C1 y 2 =4ax, B C2 x 2 =4y. P(4 ,4 ), BP A, , =0, (4 -a,4 ) (-a,1)=0, -4 +4=0, =2,a 2 =8, C +y 2 =1. (2) (1) P(4 ,8),kOP= , l kl=- . l y=- x+t,
9、5y 2 -2ty+t 2 -4=0, =4t 2 -4 5 (t 2 -4)0, t 2 0,b0),F1,F2 ,A , F1 k M,N, MAN=90 , ( B ) (A) (B)2 (C) (D) : MAN=90 =0. : F1 y=k(x+c)(k 0), y (b 2 -a 2 k 2 )x 2 -2a 2 k 2 cx-a 2 c 2 k 2 -a 2 b 2 =0. M(x1,y1),N(x2,y2), x1+x2= ,x1x2=- . MAN=90 , =(x1-a) (x2-a)+y1y2=x1x2-a(x1+x2)+a 2 +k 2 (x1+c)(x2+c)=0,
10、 (1+k 2 )x1x2+(ck 2 -a)(x1+x2)+a 2 +k 2 c 2 =0, -(1+k 2 ) +(ck 2 -a) +a 2 +k 2 c 2 =0, -2a 3 c-3a 2 c 2 +c 4 =0, -3+e 2 =0, =0, e1, e=2. 2. C:y 2 =2px(p0),A( O) , F OA , C P,Q . F x OA B, |FP| |FQ|-|OA| |OB| ( A ) (A)0 (B)1 (C)-1 (D)2 : , . 9 : OA k(k 0), OA y=kx, A( , ), B(, ),PQ:y=k(x-), x -y- =0, P(x1,y1),Q(x2,y2), y1y2=-p 2 , |FP| |FQ|= |y1| |y2| =(1+)|y1y2| =(1+)p 2 , |OA| |OB|= =(1+)p 2 , |FP| |FQ|-|OA| |OB|=0.
