要点梳理 1. 抛物线的定义平面内到一个定点 F 和一条定直线 l （ F l...

1.FlFl .F l .8.3

2.

y2=2px(p>0)y2=-2px(p>0)x2=2py(p>0)x2=-2py(p>0)pFlO00y=0x=0

e=1x0,yRx0,yRy0,xRy0,xR|PF|=|PF|=|PF|=|PF|=

1.PF02y+4=02P . PF02y+4=02PF02y+2=0PFy=-2Px2=8y.x2=8y

2.Fy2=ax (a>0)PyF12|PF|= . Px0y0y20=ax0|PF|=x0+ x0= ,|PF|= .

3.a0,aRy=4ax2 . x2= ,a>0p= ;a

4.y2=2px p . 20y2=2px20p=4.4

1Am,-3F5m. Am,-3y=-3. x2=-2py (p>0)y= , -(-3)=5,p=4,x2=-8y,Am,-3m= .

y2=2ax (a0)p=|a|x= | +m|=5 2am=9 a1=1 a2=-1 a3=9 a4=-9 m1= , m2=- , m3= m4=- .y2=2x,m= ;y2=-2x,m=- ;y2=18x,m= ;y2=-18x,m=- .

11P2-4 2Fxy=-3A|AF|=5.1P2-4y2=2px(p>0)x2=-2py(p>0).Pp=4p= y2=8xx2=-y.

2Fxy2=2px F ,0 y=-3 y2=2pxx= A( ,-2)|AF|=5 2+32=25p1,2=9,p3,4=1y2=18xy2=2x.2px=9

2y2=2xFPA32|PA|+|PF|P. PFPld|PA|+|PF||PA|+d. x=3y2=2xy= . >2A.Pl

x=- d|PA|+|PF|=|PA|+dPAl|PA|+d |PA|+|PF| P2y2=2xx=2P22.

2 2010Py2=4x.PA-11Px=-1. F10x=-1Px=-1PF.PPA-11PF10.AFP .

314y2=2px(p>0)FlABCBCxACO. y=kx+bx=my+rkOA=kOCAOC. F ,0,lx=my+ y2=2pxy2-2pmy-p2=0.Ax1,y1Bx2,y2y1y2=-p2.4

BCxCC- ,y2, 6kOC===kOA.AOCACO. 14

3 y=4x2Ax1,y1,B(x2,y2)y1+y2=5AB. x2= F|AF|=y1+ ,|BF|=y2+ ,p= ,|AB|=|AF|+|BF|=y1+ +y2+ =y1+y2+p= .

1.x0+ ;2p..2.Ax1y1Bx2y2 (1)y1y2=-p2x1x2= (2)AB ,|AB|= (3)F

1.2009x2=y . 2p=1,y= = 4y+1=0.4y+1=0

2.2010y2=24ax (a>0)M35 . l:x=-6a,M3+6a=5,a= ,y2=8x.y2=8x

3.2010OFy2=2px (p>0)A x60| | . |AF|=a|AC|=aB=30|AB|=2a|BF|=aF|FD|=p|BF|=2p|AF|=|AC|=2p.Ax0y0x0= y0=| |==

4.(2009)y2=-8x . y2=-8x,p=4,-20.-20

5.2009y2=2px(p>0)F45ABAB8p= . ABy=x- y2=2pxx2-3px+ =0,xA+xB=3p.xA+xB+p=4p=8,p=2.2

6.2008 y2=2pxp . p=4.4

7.2008FCy2=4xF1CAB.|FA|>|FB|,|FA||FB| . y2=4xF(1,0),x=-1,F1y=x-1.y2=4xx2-6x+1=0.

x1,2=|FA|>|FB|,xA=3+ ,xB=3- .|FA|=xA+1,|FB|=xB+1,

8.2009y=k(x+2)(k>0)Cy2=8xABFC|FA|=2|FB|k= . y=k(x+2)y2=8xk2x2+(4k2-8)x+4k2=0.xA,xB,xA+xB= -4,xAxB=4.|FA|=xA+2,|FB|=xB+2,|FA|=2|FB|,2xB+4=xA+2.

xA=2xB+2. xB= -2,xA= -4+2= -2.xAxB= =4.k2= ,k>0,k= ,>0.

9.2009y2=4xFxA,BFAB . F10ABAB=42.(x-1)2+y2=4.x-12+y2=4

10.20094y2=2px (p>0) y=2x,. y=2x,y= . y=2x x= x=0 y2=2px y=p, y=0(,

y= x=8p x=0 y2=2px, y=-4p y=0

8p,-4p. .p= ,y2= .,

11.2010x2=2py p>0F30,ABAy . ,AAx,BBx,AAFOBB, xA0,ABy=xtan 30+ ,

x2=2pyx2- -p2=0,xA+xB= ,xAxB=-p2xAxB=-p2=-= x2A+x2B+2xAxB3x2A+3x2B+10xAxB=0x2Bx2B0 , .xA+xB= ,xA>-xB,

12.2010 y2=8xFAB. 1Fl 2 ABmxP|FP|-|FP|cos 2 . 12p=8, =2,F20x=-2.

2AxAyABxByBABk=tan ,y=k(x-2),y2=8x,k2x2-4(k2+2)x+4k2=0,xA+xB= ,mABExE,yE)xE=m

y=0,PxP=|FP|=xP-2= ,|FP|-|FP|cos2 = ,.

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