解答题题型突破五-解析几何

......

.

Ⅰ

x+y+x-=

A

l

B

x

l

A

CD

BAC

AD

E.|EA|+|EB|

E

E

C

l

C

MN

B

l

A

PQ

MPNQ

.|AD|=|AC|EBACEBD=ACD=ADC|EB|=|ED||EA|+|EB|=|EA|+|ED|=|AD|.

Ax++y=|AD|=|EA|+|EB|=.

A-B|AB|=

E

+

=y.

l

x

l

y=kx-kMxyNxy.

k+x-kx+k-=

x+x= xx=

.|MN|=

|x-x|=

.

B

l

my=-

x-

A

m |PQ|= = .

MPNQ

S=

|MN||PQ|= .

l

x

MPNQ

.

l

x

x=|MN|=|PQ|=

MPNQ

.

MPNQ

.

kPkP=

=-

+x=y>

Cy=-x+y

x

AB

A

kPkP=

=-

+x=y>DOO

PB-.

P

C

B

l

CC

MQ

ABAMQMAQ

l

.

A-B.

Pxyy>∵DOPA∴kOkB=kAkB.∴

P

C

+x=y>.

C

+x=y>.

l

x

y=kx-k

Ck+x-kx+k-=. *

Mxy∵

l

B∴x=

*.

x=

y=

∴∴

M

.

Q-k--k-k.=∴ =

=-k-k-k.eq

\o\ac(△,∵)

AMQMAQ∴ > k-k+>∴k-k+<

k>-

.

y'=-x|==-

l

B-.

l

k<-∴

l

.

..

Ⅱ

O

M

C

+y=

M

x

N

P

=.

P

Q

x=-

=

P

OQ

l

C

F.

PxyMxy

Nx

=x-xy

=y.

=

x=xy=

y.

Mxy

C

+

=.

P

x+y=.

F-.

Q-tPmn

=-t

=--m-n

=+m-tn

=mn

=--mt-n. =

-m-m+tn-n=.

m+n=

+m-tn=

=

.

P

OQ

P

OQ

l

C

F.

Ⅲ

xOy

y=x+mx-

x

AB

C.

m

ACBC.

ABC

y.

ACBC.

AxBx

xx

x+mx-=

xx=-.

C

AC

BC

=-

ACBC.BC

BC

y-

=x .

x+x=-m

AB

x=-

.

+mx-=

ABC

r=.

y

=

ABC

y

.

AB

x

y

R

AB

=

|

|=+

.

R

C.

M-N

F

C

PQP

x

MPNQ

kk.

RxyAmBn

=

x-my=

-xn-y

①|

|=+

m+n=+

②①②

+

=

R

C.

PQ

x=my+

PxyQxy

m+y+my-=

=

=

=

=

=

=

=

=

=

=

myy=

y+y.

.

..

Ⅱ

A

E

+

=

kk>

E

AM

N

EMANA.|AM|=|AN|AMN

|AM|=|AN| <k<.

Mxy

y>.

AM

.

A-

AM

y=x+.

x=y-

+

=

y-y=

y=

y=

y=

.AMN

eq

\o\ac(△,S)

AMN=×

×

×

=

.

AM

y=kx+k>

+

=

+kx+kx+k-=.

x-=

x=

|AM|=|x+| = .

AN

y=-

x+|AN|=

.

|AM|=|AN|

=

k-k+k-=.

ft=t-t+t-

k

ft.f't=t-t+=t-

ft+∞.

f = -<f=>

ft+∞

k

<k<.

P

C

+

=a>b>F.

C.

C

P

DE

O

PDPE

y

MN

MN

y=

.

F'-

c=.∵a= + =∴a=b= = ∴

C

+

=.

DE

P.∵DE∴

DmnE-m-nm±.

MN

y=

G H

t>∴GMGN.

PDy-

=

x-.

x=

y=-

+

M .

PEy-

=

x=

y=-

x-.+

∴N .=

=

=

∵GMGN∴

==t+∴ ==t+∵ +

=

m+n=n-=-m∴t-

=

t=

.∴G H

∴|GH|= .∴

MN

y=

.

Ⅰ

xOy

ly=tt

y

M

Cy=pxp>

PM

P

N

ON

C

H.

H

MH

C.

MtP .

N

M

P

N

ON

y=

x

y=px

px-tx=

x=x= .

H .

N

OH =.

MH

C

H.

MH

y-t=

x

x=

y-t.

y=px

y-ty+t=

y=y=t

MH

C

H

MH

C.

xOy

Cx=pyp>

F

M

+

=a>b>

F

C

M

E |EF|=

.

C

M.

m

Pm

C

AB

F

AB

m.

C

E |EF|=

.

+

=

p=

Cx=y

Ft=

.

M

+

=.

C

x=y

M

+

=.

m

AB

AB

y=kx+m.

y

x-kx-m=.

m>

k+m>.

AxyBxy

x+x=kxx=-m

y+y= =

=k+myy=

=m.

=xx+yy-

=xx+yy-y+y+=m-m+-k.=xy-

<

m-m+<k.

k

m-m+<

- <m<+ .

m>

- <m<+ .

m

m- + .

+

=a>b>

e=

FF|FF|=

MxyNxy-

.

C + .

c= ∵e=

=

∴a=b=a-c=

C

+y=.∵

=-

∴xx=-yy∴ = . ①

+ =

+ =∴-

= -

= ∴ = - - = . ②①②- - = + =.

+

=a>b>

Qx+y-x-y+=

Q

CP

C

.

C.

P

l

C

AB

eq

\o\ac(△,S)

AQB=AQB

l

.

C

Fc|PF|=

c= .

Q

C

+

=.

a-b=a=b=

C

+

=.

eq

\o\ac(△,S)

AQB=AQB

|QA||QB|AQB=AQB|QA||QB|AQB= =.①

l

x

=- --- -=+-=

l

x=.②

l

x

l

y=kx+

y

+kx+kx-=

AxyBxy

x+x=

xx=

=

x-y-x-y-=

y=kx+y=kx+x-x-+kxx= + +=

k=

l

x-y+=.

l

x=

x-y+=.

y

l

AB

y

l

.

lx=my-

y=px

y-pmy+p=. *

=.

AxyBxy

y+y=pmyy=p

xx=

=.

=

xx+yy=

+p=

p=

y=x.*

y-my+=

y+y=myy=.

AB

Mxy|AB|=x=x+x=my+y-=m- ①|AB|= |y-y|= ②①②+mm-=m-

m=

m=± .

l

x+ y+=

x- y+=.

+

=a>b>

FF

FPQ

PF

x+y=.

PO

RPQR.|PF|

M

eq

\o\ac(△,PF)F|OM|=

|PF||OM|=-

|PF|.∴

|PF|=-

|PF||PF|+|PF|=

a=

e=

∴c=b= .∴

+

=.

kQ

PQx=my-PxyQxy.

m+y-my-=.eq

\o\ac(△,S)

PQR=eq

\o\ac(△,S)

POQ=|y-y|= =t=

.=

t=

in=.∴eq

\o\ac(△,S)

PQRax=.

xOy,F

,M

C

Q

Q

C

.

C.

M

MQ

C

M

M.

F

Q

OF

y=

C

y=-

=

p=.

C

x=y.

M x>

C

M

y' =x= ' =x=x

MQ

y-

=xx-x.

y=

x=

+

Q .|QM|=|OQ| +

=

+

=

.

x>

x=

M .

M

MQ

C

M.

-x+y

y

l

CD.

CxyDx

CxyDxy

F

CD

E

>x-x-+yy>.