1Fl(Fl)Fl.

2()

y22px(p>0)y22px(p>0)

y22px(p>0)y22px(p>0)x0yRx0yRxO(0,0)e1

x22py(p>0)x22py(p>0)

x22py(p>0)x22py(p>0)y0xRy0xRyO(0,0)e1

(1)ppp(2). (3)

Px20M(40)2P()ABC DPx4M(4,0)D.D[1]

Pxy40M(2,2)P()A BC DM(2,2)xy40|PM|Pxy40PMxy40A.A

(1,0)x1()Ax2y21 Bx2y21Cy24x Dx0(xy)x(1) y24xC.CC(1,0)x1C(1,0)x1p2y24x.

[2]

Py24xQx2(y4)21PQP()

A5

B8 C.eq \r(17)1 D.eq \r(5)2

[]y24xF(1,0)x2(y4)21C(0,4)Pdd|PF||PQ|d|PQ||PF|(|PC|1)|PF||CF|1eq \r(17)1.

9Q

[3]

[4]

eq \f(x2,m)eq \f(y2,n)1(mn0)2y24xmn

()

A.eq \f(3,16)

B.eq \f(3,8)

C.eq \f(16,3)

D.eq \f(8,3)

A

eq \b\lc\{\rc\ (\a\vs4\al\co1(\f(\r(mn),\r(m))2,\r(mn)1))eq \b\lc\{\rc\ (\a\vs4\al\co1(m\f(1,4),n\f(3,4))) .

mneq \f(3,16).A.

y22px 1p ()A2B2 C4D4D

a26b22ceq \r(a2b2)2

(2,0)eq \f(p,2)2p4.

Cy28xFxKAC|AK| |AF|AFK()A4 B8 C16 D32y28xF(2,0)x2K(2,0)[5]

(x2)2y22[(x2)2y2]y2x212x4y28xx2y4

B|AK| |AF|.

[6]

[1]yax21yxa()

A.eq \f(1,8)B.eq \f(1,4)

C.eq \f(1,2)

D1

B

1yax21yxeq \b\lc\{\rc\ (\a\vs4\al\co1(yax21,yx))ax2x10(1)24a0aeq \f(1,4).

2(x0x0)yax21y|xx02ax02ax01.

(x0x0)x0axeq \o\al(2,0)1

aeq \f(1,4).B.

P 0 4 y2=2x 3

[7]

ABy22px(p>0)FA(x1y1)B(x2y2)

(1)x1x2eq \f(p2,4)

(2)|AB|x1x2peq \f(2p,sin2)(ABx)

(3)SAOBeq \f(p2,2sin)

(4)eq \f(1,|AF|)eq \f(1,|BF|)

(5)AB

.

(1)y22px(p>0)Feq \b\lc\(\rc\)(\a\vs4\al\co1(\f(p,2)0))

ykeq \b\lc\(\rc\)(\a\vs4\al\co1(x\f(p,2)))(k0)

eq \b\lc\{\rc\ (\a\vs4\al\co1(yk\b\lc\(\rc\)(\a\vs4\al\co1(x\f(p,2))),y22px))xky22pykp20

y1y2p2x1x2eq \f((y1y2)2,4p2)eq \f(p2,4).

kxeq \f(p,2)

y1py2py1y2p2x1x2eq \f(p2,4).

y1y2p2x1x2eq \f(p2,4).

(2)|AF|Axeq \f(p,2).

|AF|x1eq \f(p,2)|BF|x2eq \f(p,2).

|AB||AF||BF|x1x2p.

ykeq \b\lc\(\rc\)(\a\vs4\al\co1(x\f(p,2)))xeq \f(1,k)yeq \f(p,2).

x1x2eq \f(1,k)(y1y2)p

y1y2eq \f(2p,k).x1x2eq \f(2p,k2)p

|AB|eq \f(2p,k2)2p2peq \b\lc\(\rc\)(\a\vs4\al\co1(1\f(1,k2)))2peq \b\lc\(\rc\)(\a\vs4\al\co1(1\f(1,tan2)))eq \f(2p,sin2) .

(3)

SAOBSAOFSBOF

eq \f(1,2)|OF||AF|sineq \f(1,2)|OF||BF|sin

eq \f(1,2)|OF|sin(|AF||BF|)

eq \f(1,2)|OF||AB|sin

eq \f(1,2)eq \f(p,2)eq \f(2p,sin2)sineq \f(p2,2sin).

(4)eq \f(1,|AF|)eq \f(1,|BF|)eq \f(1,x1\f(p,2))eq \f(1,x2\f(p,2))

eq \f(x1x2p,x1x2\f(p,2)(x1x2)\f(p2,4))

x1x2eq \f(p2,4)

eq \f(1,|AF|)eq \f(1,|BF|)eq \f(2,p).

(5)ABM(x0y0)AMBCND

|MN|eq \f(1,2)(|AC||BD|)eq \f(1,2)(|AF||BF|)

eq \f(1,2)|AB|. AB

(1)(). ANB90CDABF. (2)

y22px(p>0)FP1(x1y1)P2(x2y2)P3(x3y3)2x2x1x3()A|FP1||FP2||FP3|B|FP1|2|FP2|2|FP3|2C2|FP2||FP1||FP3|D|FP2|2|FP1||FP3|

2x2x1x3p

P1P2P32|FP2||FP1||FP3|.C

[8]

y22px(p>0)1ABAB2()

Ax1 Bx1 Cx2

Dx2

[]A(x1y1)B(x2y2)AB(eq \f(x1x2,2)eq \f(y1y2,2))eq \f(y1y2,2)2eq \b\lc\{\rc\ (\a\vs4\al\co1(y\o\al(2,1)2px1,y\o\al(2,2)2px2))yeq \o\al(2,1)yeq \o\al(2,2)2p(x1x2)kABeq \f(y1y2,x1x2)eq \f(2p,y1y2)eq \f(p,2)kAB1p2y24xx1B.

[9]

Cyax21(a0)lyx0a________A(x1y1)B(x2y2)Cl(x1x2)AByxb.

x1x214a(1b)>0.ABM(x0y0)

x0eq \f(x1x2,2)eq \f(1,2a)y0x0beq \f(1,2a)b.

Mleq \f(1,2a)eq \f(1,2a)b0

beq \f(1,a)a>eq \f(3,4).

[10]

xOyly24xAB.

(1)leq \o(OA,\s\up6())eq \o(OB,\s\up6())________

(2)eq \o(OA,\s\up6())eq \o(OB,\s\up6())4l________

(1)(1,0)lxty1y24xxy24ty40A(x1y1)B(x2y2)y1y24ty1y24x1x2y1y2(ty11)(ty21)y1y2t2y1y2t(y1y2)1y1y24t24t2143.

(2)lxtyby24xxy24ty4b0A(x1y1)B(x2y2)y1y24ty1y24b. x1x2y1y2(ty1b)(ty2b)y1y2t2y1y2bt(y1y2)b2y1y24bt24bt2b24bb24b.b24b4b24b40b2.l(2,0)(1)3(2)(2,0)

ABCy22px(p>0)FABxxD.

(1)DFABeq \f(,4)eq \f(\o(OA,\s\up6())\o(OB,\s\up6()),p2)(O)

(2)|AF||BF|8ABQ(6,0)C

[]A(x1y1)B(x2y2)

(1)AByxeq \f(p,2)

eq \b\lc\{\rc\ (\a\vs4\al\co1(y22px,yx\f(p,2)))x23pxeq \f(p2,4)0

x1x23px1x2eq \f(p2,4).

eq \f(\o(OA,\s\up6())\o(OB,\s\up6()),p2)eq \f(x1x2y1y2,p2)eq \f(x1x2\b\lc\(\rc\)(\a\vs4\al\co1(x1\f(p,2)))\b\lc\(\rc\)(\a\vs4\al\co1(x2\f(p,2))),p2)

eq \f(2x1x2\f(p,2)(x1x2)\f(p2,4),p2)eq \f(2\f(p2,4)\f(p,2)3p\f(p2,4),p2)eq \f(3,4)

(2)xeq \f(p,2)|AF||BF|x1eq \f(p,2)x2eq \f(p,2)x1x2p8

x1x28p

Q(6,0)AB|QA||QB|

(x16)2yeq \o\al(2,1)(x26)2yeq \o\al(2,2)

yeq \o\al(2,1)2px1yeq \o\al(2,2)2px2

(x16)22px1(x26)22px2

(x1x2)(x1x2122p)0

x1x2x1x2122p8p122p0

p4y28x.