高中数学圆锥曲线的知识点总结

高数圆曲部知点理一方的线C()f(,y)

(2)C(x)(x,y)00

(x,y)xy)0000

f(,)0

1

2

fx,)1

f(xy2

(x,y00

1

2

{

fxy)00f(xy)00

n

n

.二圆、义

{}

Or.、程(1)

C(b

r

())r2

r

x

2

y

2

2(2)①

D22F

x22F

(

DD,)22

xDxEy

D(x)2)2

F②

D

2

F

(

D,)22③

D2F

.3

C(b

r

M

(,)00

|r

M

|MCrMMC|r

(x0

220

4①没②(ii)r.A2

C(b

By

-1-

三圆曲的一义

(x)

F(,0)

l(e0)

.

F(,0)

l

.0

e

e

四椭、曲、物：

1

2

F1

F|)1

F|)1

e.

e.

(e

{M|MF||,12FFa}1yBM

{|MFMF2FF|}

{MF|M到线的}

AF

b

ac

FA

x

ac

B

x=

ac

xy2

(

a

xy2(b0)22

y

sin(参心角）

asec参数角）

xy

(t)

yR

x0-2-

22

O

O(a,0)

(

(a,0)

(

(0,0)b

y

y

2b

虚

2

(c1

(,0)(c,0)2

2

pF(2

x

2c

x

2c

px2

.

.

y

ba

x

2(c

2

2

)2(

2

2

)

|PF|1

)1|)2

PF|

p2

a

2

ba

2

2p

(0a

a

e

【注】曲：1x

e.2.-3-

ya

22y2xayaba22y2xay3

22

y

22

22

y

22

ya

a

b

.【注】物：

ypx

x

p2

ypx(

0)

x

p2

x

2

(p

(0)

y

p2

x

2

2(p

(0)

y

p2

.2

y

2

(p0)

x,y)00

M

MFx0

p2

3

y

2

(p0)

2p五坐的换).2M

x

(,y)

x'y'

(

'y

)

OxOy

(,)

xx'yy(.六椭的用论

F12

P.

(,0)1

(c,0)2

(xy)00

a2

x2b2y

'

b2xk'2(y)

2x0y0-4-

2PF212ay2PF212ay

k1

PF

yy0,k0xx0022tan()2tan

cy0

,000

x2b2

xy002b2

ab2

x22y

'

b2xk'2(y)

2x0y0

xy00a22

,000

x2b2

P

、P12

12

xy02b2

)(x))(y)00

2

(xx))(0

2

x(22

、P1

1

S

PF

2

2

.

PFPF1

2cosc

2

m)

2

mn

-5-

OPQOPQ

221

F

1sinsin222

11abC22

x(a22

|a1

(

(1

(c2

M()00

).

MF|2)y2x210

2x2(2)02MF|10

|a1

x2222

(xy)0

kOMAB

22

AB

x2y

y(x)y0

x12

a

2

k2xka022

2

y

0x0

2x0y0

,000

x2b2

0

xyy2002b22

x(a22

P、Q

POQ

1111OP|2OQ2b2

;2

|OP|2|2

2ab2;3S22a22:

ykx(

2k22kma2x22b

x12

2m2222k

,yy2(x)12

2

xyy12

ma2a2

22

211OQ2||22|OP2|OQ|2OP|2OQ2PQ|abab2

OP|2|2

11|OP|2OQ2|))(2b2

)

2-6-

22OPQOP|2OQ222OPQ

2222322a2

2七双线常结：、PPTF12

P内角P(x,y)000

x2(ab

xyy0a2b

000

x2(b0)b

、P12

12

xyy0a2b

x(ab22

FP1

PF1

S

2

cot

2

x2(b22

(

(1

(c2

M()00

|MF||exM(xy)1000

||1020

x(ab22

x,y)00

AB

2x

000

x2(b0)b

0

xyy22002bb

x2(b0)OP、QO221114ab2a1;2OP||;3SOP22b222b八抛线常结：ay2(

acb)aaAB

y

2

(p(),B(x,y)11

1

x1

2

,y1

22

AB|1

2sin

弦A的倾斜)-7-

2x12121yyy2x12121yyy

y(x

p2

)

k2pkp)2k2

x111

2

()1

2

x12

p(kk

22

|AB1

pp)223

12FA|

11p212|FA||FBp2x(x)224AB5

AO

B

'OA'

6

2px(p