1 100053 yjyj118@sina.com ;, oxy (x,y),
, P x o,y o, l Ax+By+C=0(A B 0), P l d. P l d : 1. l k k = A B. l k` k` = B A 3. P l` k` = B A, l` y y o = B A (x x o) 4. l l` P` P` ( A ( B yo + C) B xo ) A yo A B xo B C) (, ) A + B A + B 5. P` x1,b1
6. PP` = x x ) + ( y ) ( 0 1 0 b1 P l d = A x o + B y A o + B + C A B=0 3
1 x F 1 F F 1 F M(x y) c (c>0) M F 1 F a F 1 F ( c 0) (c 0) 3 M MF 1 + MF =a 4 (x+c) +y + (x c) +y = a 5 M (x+c) +y (x c) +y m n (x+c) +y + (x c) +y = a = (x+c) +y (x c) +y +x +y +c =4a (x+c) +y (x c) +y =4a - x +y +c (x+c) +y (x c) +y 4a - x +y +c m n m -n =0, 4
16 (a c )x +a y a +c =0 (a c )x +a y = a (a c ) x a + y (a c ) =1 a c =b (b>0) b x + a y = a b x a + y b =1 (a> b>0) B m e 0<e F 1 e 5
B m 3 4. I. 0<e<1 II. e=0 III. 1<e x 9 + y 4 =1 1 6
H x 0,y 0 x 0 I. H 9 + y 0 4 =1 II. x 0 H 9 + y 0 4 1 x 0 III. H 9 + y 0 4 1 " " " " " " 7
x y P + = 1 A 1 1 PA 3 PA PA P ( x, y ) PA 0 0 x0 ( 3,0) y 0 (0, ) y = x 3 0 0 PA = ( x0 + 1) + ( y0 1) = ( x0 + 1) + ( x0 1) = ( x0 + 1) + ( x0 1) 3 3 PA PA = f(x) 6 x0 3) x0 f(x)= + + x0 3 3 + 4, x 0 ( 3,0) 8
x0 ( 3,0) 4 3 0 6 0 0 0 = x + x + 1x 18x 7 0 0 3 0 0 0 = x + x + 3x 18x 7 0 [ 0 0 0 0 0 0 = x + 3x + a( x + 3x ) + a] + (3 a) x (18+ a) x 7 a 0 ( 3 a) x0 (18+ a) x0 7 a = 18 + a 4 3 a)( 7 a) = 0 a ( 3 a) x0 (18+ a) x0 7 a a x 0 ( 3,0) 9
x + y = 1 A, 3 F 16 1 P AP + PF 1 c =, e = l : x = 8 P PN l 1 PF = e PN = PN AP + PF = AP + PN > AN A P N AN l 10 P A y = 3 x = 3 P( 3, 3) AP + PF I. II. III. AP + PF AF 1 10
AP + k PF k>0 AP + PF PF AP + k x= PF y= AP y+x=m y+kx=n x,y,m n 1 000 1-91 6 3 1 1997 5 1 4 5 11