1、 1 6 1,3,6 ( ) 2,7,10,14,15 ( ) 4,5,8,11 ( ) 12,13 ( ) 9,16 ( :30 ) 1. (x 2 +y 2 -4) =0 ( C ) : x+y+1=0. x+y+1=0 x 2 +y 2 -4=0 x+y+1=0 , C. 2. A(-2,0),B(1,0), P |PA|=2|PB|, P ( B ) (A) (B) (C) (D) : P(x,y), =2 , x 2 +y 2 -4x=0, D 2 +E 2 -4F=160, P . 3.(2015 ) xy 2 -x 2 y=8x ( B ) (A) y (B) (C) x+y=0
2、 (D) x-y=0 : -x x, , y ,A ; -x x,-y y, , ,B ; -x y,-y x, , x+y=0 ,C ; x y,y x, , y=x ,D . B. 4.(2016 ) P 2x-y+3=0 , M(-1,2),Q PM , |PM|=|MQ|, Q ( D ) (A)2x+y+1=0 (B)2x-y-5=0 (C)2x-y-1=0 (D)2x-y+5=0 2 : Q(x,y), P (-2-x,4-y), 2x-y+3=0 Q 2x-y+5=0. 5. (x+1) 2 +y 2 =25 C,A(1,0) ,Q . AQ CQ M, M ( D ) (A)
3、- =1 (B) + =1 (C) - =1 (D) + =1 : M AQ , |AM|=|MQ|, |MC|+|MA|=|MC|+|MQ|=|CQ|=5, M C,A . a=,c=1, b 2 =a 2 -c 2 = , + =1. 6.(2015 ) mx 2 +4y 2 =4m e 2x 2 -5x+2=0 , ( B ) (A)4 (B)3 (C)2 (D)1 : e 2x 2 -5x+2=0 , e=2 e=.mx 2 +4y 2 =4m +=1, x , =, m=3; y , =, m= ; x , - =1, =2, m=-12. 3 . 3 7. ,O , A(-2,1)
4、,B(-1,3), C = + , , 0,1 + =1, C . : C(x,y), + =1 2x-y+5=0, x=-2 - =-2 -(1- )=- -1 -2,-1, C 2x-y+5=0,x -2,-1. :2x-y+5=0,x -2,-1 8. ABC A(-5,0),B(5,0), ABC x=3 , C . : ,|AD|=|AE|=8, |BF|=|BE|=2, |CD|=|CF|, |CA|-|CB|=8-2=6, , A,B , 6 , - =1(x3). :- =1(x3) 9.(2015 ) ,O ,A(1,0),B(2,2), C = +t( - ), t R,
5、C . : C(x,y), =(x,y), +t( - )=(1+t,2t), t C y=2x-2. 4 :y=2x-2 10. M(-1,0),N(1,0), P , , , P . : P (x,y), =(x+1,y) (2,0)=2(x+1), =(-1-x,-y) (1-x,-y)=x 2 +y 2 -1, =(-2,0) (x-1,y)=2(1-x), 2 = + , 2(x 2 +y 2 -1)=2(1+x)+2(1-x), x 2 +y 2 =3, 0 2(1-x)-2(1+x)0, P x 2 +y 2 =3(x0). 11.(2015 ) O:x 2 +y 2 =4, A
6、( ,0), AB O, B . (1) ; (2) AB O C,D , B CD , AB . :(1) AB M, N, OM,MN( ), |OM|+|MN|=|ON|=2, A y A , A B, |A B|+|AB|=2(|OM|+|MN|)=4. B A ,A , 4 . ,a=2,c= ,b=1, +y 2 =1. (2) B CD , OB CD, . B(x0,y0), x0(x0- )+ =0. 5 + =1, x0= ,y0= . kOB= ,kAB= , AB y= (x- ), x-y- =0 x+y- =0. ( :15 ) 12.(2016 ) P(x,y)
7、x y A,B , Q P y ,O . =2 , =1, P ( A ) (A)x 2 +3y 2 =1(x0,y0) (B)x 2 -3y 2 =1(x0,y0) (C)3x 2 -y 2 =1(x0,y0) (D)3x 2 +y 2 =1(x0,y0) : A(a,0),B(0,b),a0,b0, =2 , (x,y-b)=2(a-x,-y), a=x0,b=3y0. Q(-x,y), =1, (-x,y) (-a,b)=1, ax+by=1. a,b ax+by=1 x 2 +3y 2 =1(x0,y0). 13.(2015 ) , xOy ,A(1,0),B(1,1),C(0,1).
8、 f xOy P(x,y) uO v P (2xy,x 2 -y 2 ), P ABC , f , P ( D ) : P AB ,x=1, P (x ,y ), (0 y 1) 6 y =1- (0 x 2,0 y 1). P BC ,y=1, (0 x 1), y = -1(0 x 2,-1 y 0), P D , D. 14. P F(a,0)(a0) y A B, ABP , P . : P(x,y), P R, ABP , P y d= R, |x|= R. R=|PF|= , |x|= . (x+3a) 2 -3y 2 =12a 2 , - =1. : - =1 15.(2015
9、) P (x, y) A(-2,0),B(2,0), PA,PB k1,k2 k1k2=-. (1) P C ; (2) l:y=kx+m C M,N, OM ON , O l (O ). :(1) P(x,y), =-, x 2 +4y 2 =4, 7 +y 2 =1(x 2). (2) M(x1,y1),N(x2,y2) y (4k 2 +1)x 2 +8kmx+4m 2 -4=0, =(8km) 2 -4(4k 2 +1)(4m 2 -4)0, 4k 2 +1-m 2 0. x1+x2=- , x1 x2= , OM ON, x1 x2+y1 y2=0, x1 x2+(kx1+m)(kx
10、2+m)=(1+k 2 )x1 x2+km(x1+x2)+m 2 =0, (1+k 2 ) +km (- )+m 2 =0, m 2 =(k 2 +1) 4k 2 +1-m 2 0, O l d= , d 2 = =, d= . 16.(2015 ) C(2,0) C y= x(x 0) , l C , A,B, AB M . : l y=kx+b. A(x1,y1),B(x2,y2),M(x,y), A( , ) (k 0). B( , ), 8 k=,b= , C y= x , C r= . AB:kx-y+b=0 C , = , 2k 2 +4kb+b 2 -2=0, (y 2 -x 2
11、 ) 2 +4x(y 2 -x 2 )-2(y 2 -x 2 )=0, y 2 x 2 , y 2 -x 2 +4x-2=0, (x-2) 2 -y 2 =2(y 0), l x , AB M(2 ,0) , AOB . 5 1.(2016 ) C M, M A(-5,0),B(5,0) 8, C , ( B ) (A)x+y=5 (B)x 2 +y 2 =9 (C) +=1 (D)x 2 =16y : M , M , . : M A(-5,0),B(5,0) 8, M A(-5,0),B(5,0) , -=1(x 4). A. x+y=5 (5,0), ; B. x 2 +y 2 =9 (0,0), 3, M , ; C. + =1 (5,0) ; D. x 2 =16y -=1, y-=1, y 2 -9y+9=0, , . B. 2.(2015 ) |x|+y 2 -3y=0 ,y . 9 : -x x, , , y 2 -3y=-|x| 0, y . : -x x, , |x|+y 2 -3y=0 x=0, y 2 -3y=-|x| 0, 0 y 3, y 0,3. :x=0 0,3
