解析几何,吕林根,课后习题解答一到五

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14§2.4®¯]^ḄZ[1ஹ\☢È=cY/+y?-2x=0ḄÉᐳ`ÊᡂË᪵ḄWX஺!:2ஹᢣk0ᑡ]☢YÍᙶ᪗☢Ḅ^ᑖzLlm]^p(1)x2+y2+16z2=64(2)x2+4>,2-16z2=64(3)x2-4y2-16z2=64(4)x2+9y2=lOz!q3.0ᑡ®¯]^$Íᙶ᪗☢ḄÑÒÃ☢Z[஺x2+y2-z=0[x2+z2-3yz-2x+3z-3=0=0পீ;(2)\z=x+l[y-z+l=Ox+2y+6z=5[x1+y24-z2=1(3)×(4)3x-2y-10z=7[x2+(y-l)24-(z-l)2=1

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181_111úᙶ᪗¼`ᑮ\☢Ḅbcu஺""#:§3.2\☢Y`Ḅ÷ᐵñý1.þÿᑡ☢Ḅ(1)M(—2,4,3),71\2x—y+2z+3=0(2)M(l,2,-3),7t:5x-3y+z+4=0."2.#ᑡᔜḄᙶ᪗(1)ᙠy()*ᑮ☢2+2y-2z-2=0Ḅ,-4.ᓫ0Ḅ(2)ᙠz()*ᑮM(l,-2,0)1ᑮ☢3x-2y+6z-9=02,Ḅ(3)ᙠx()*ᑮ☢12*-16)>+152+1=02%+2ு82-1=02,Ḅ஺"3.:;<☢=Ḅ<.⚔?S(0,6,4),A(3,5,3),3(—211,—5),C(1,—1,4),CDE⚔SᔣG☢ABCᡠJḄK஺"4.#LMᙠC(3,-5,2)*1☢2x—y-3z+11=02ᑗḄᳫ☢PQ஺"

195.#RSx(ᐸ1M(5,4,13)28.ᓫ0Ḅ☢PQ஺"6.#1ᑡᔜV☢2,ḄḄWX.প3x+6y—2z—7=04x—3y—5=0(2)9x-j+2z—14=09x—y+2z+6=0.".9ᑨ^M(2-11)N(12-3)ᙠᵫᑡ2a☢ᡠ᪀ᡂḄd8.e☢fᑁ,hiᙠ2je☢fᑁkᡈiᙠV⚔Ḅe☢fᑁm(1):3x—y+2z—3=01nx—2y—z+4=0(2)o2x-y+5z-l=01423x-2y+6z-l=0"10p#ᵫ☢q2x-y+2z—3=01»23x+2y-6z-l=0ᡠᡂḄe☢fḄfᑖPQkᙠte☢fᑁᨵ(1,2,-3)"

203.3v☢Ḅ2ᐵ0x1.ᑨ^ᑡᔜVyzḄ2ᐵ0x(1)x+2y-4z+l=012-z-3=042(2)2x-y-2z-5=C^x+3y-z-l=09(3)6x+2y-4z-5=09x+3y-6z--=0o"2.ᑖ^ᙠᑡᩩ|}~/kk஻Ḅ(1)(/-3)x+(+l)y+(஻-3)z+8=0(m+3)x+(஻-9)y+(/-3)z-16=0⊤d8☢(2)++3z-5=01Zx-6y—6z+2=0⊤e☢(3)Zx+y-3z+l=O17x+2y-z=0⊤e2ᚖyḄ☢஺"3.#ᑡv☢Ḅ(1)19x-4y+8z+21=0,19x-4y+8z+42=0(2)3x+6y-2z-7=0,3x+6y-2z+14=0஺"

214.#ᑡᔜ☢ᡠᡂḄf(1)x+y—11=0,3x+8=0(2)2x-3y+6z—12=0,x+2y+2z—7=0஺"5.#ᑡ☢ḄPQ(1)RSM(0,0,1)(3,0,0)*1ᙶ᪗☢xOyᡂ60°fḄ☢;(2)Sz(*1☢2+ஹ82-7=0ᡂ60°fḄ☢."§3.4yzḄPQ1.#ᑡᔜyzḄPQ(1)RSA(-3,0,1)8(2,-5,1)Ḅyz;(2)RSMo(/kyokZo)*-v2a☢AjX+gy+Gz+0=0(i=1,2)Ḅyz;(3)RSM(l-5,3)*1,y,Z(ᑖ^ᡂ60°,45°,120°Ḅyz(4)RSM(1,0-2)*1vyz—=2==)e=—ᚖyḄyz;(5)RSM(2-3-5)*1☢6x-3y-5z+2=0ᚖyḄyz஺

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232x4-y-z+l=0x+z-6=0(1)<ফ13x—y—2z—3=02x-4y-z+6=0y-z=0(3)<-x=2"5.8z1ᙶ᪗(Ḅfᑖ^?a,/?,/.³´sin2*4a+sin2/?+sin2y=2.³§3.5yz1☢Ḅ2ᐵ0x1.ᑨ^ᑡyz1☢Ḅ2ᐵ0x(1)==14x—2y—2z=3-2-73(2)2=-^-=13x—2y+7z=83-275x-3y+2z-5=0(3)14x-3y+7z-7=02x-y-z-l=0x=t(4)

24x-2t+2¾2¿yzÀy=-4t-51☢Â+ÿk+62-7=0ᚖy஺z=3r-1"A.x+B,y+C,z=Q4.Å~yz1171☢¾A+A,¿x+¾ὡ+B,¿y+¾G+C,¿z=OḄ2Ax+By+Cz=02220x஺"5.Èyz1ᙶ᪗☢Ḅafᑖ^?³´cos'4+cos?4+cos?v=2.³´6.#ᑡᳫ☢ḄPQপ1☢x+2y+3=02ᑗ-M(1,1,-3)*ÊËr=3Ḅᳫ☢(2)1v☢6x-3y-2z-35=06x-3y-2z+63=0Ì2ᑗ*-ᐸL¥82ᑗ-M(5,T—1)Ḅᳫ☢.":

253.7yzḄ2ᐵ0xA/+By+Gz+Dj=0{1.yzPQḄÎᦪÐÑÒÓᩩ|ÔÕ:AX+By+Cz+£>2=0222¾1¿yz1x(2a¾2¿yz1x(¾3¿yz1x(Öᔠ஺"2.}~2ᑡvyz2a:3x-y+2z—6=0(1)x+4y+Az-\5=0ஹØ81y+1z—1,,,(2)-----=------=-------1x+l=y=l=z1271"3.ᑨ^ᑡᔜVyzḄ20xk᝞Úi2aḄᡈḄyz#¼ÛᡠᙠḄ☢᝞ÚiÜ☢yzk#¼Û¥Ḅ஺পx-2y+2z=0I_x+2y-z-ll=03x+2y-6=0,2x+z-14=0x-3_y-8z3τ.x+3y+7z—6(2)-1-3-2-4x=tC,—x—1y—4z+2(3)y=2f+11----=J-----=-----417-5z=—t—2":

264.Þ~vÜ☢yz==2=11)'=)¦=£,p#¼ÛḄàᚖzPQ஺210101"5.#ᑡᔜVyzḄfx-l_y+2_z-5i-^x_y-3_z+l(1)----=-----=-----â—=-----=------3622963x-4y-2z=0|4x+y-6z-2-0(2)ீ1'2x+y—2z=0[y—3z+2=0"6.Èdd'ᑖ^iᙶ᪗ᑮM¾a,åc¿M'Md,b',c'=Ḅk³´æact+bb'+cc+dd'çkyzMM'RS³7.#RSP¾l,0,-2¿*1☢3x-y+2z-1=0k¢1yz—=e=24—21aḄyzPQ."

27x+V4-Z=1.8.#RSP¾4,0,-l¿*1vyzÀk142kx—y—8z=e34Ì2aḄyzP2x-y-z=2)Q."9.x+22V-1z-3#1yz——=—=——*ᑡvyz2aḄyz.871z=5Ø-6fz=2x-4z=4x+3[z=3y+5x=2t-3x=5/+10(2)

282x—2y+z+3=02.#”(2,3,—1)ᑮyzkḄ஺3x—2y+2z+17=0"§3.8☢ï1.#RS☢4%-ð+32-1=08+5ð-2+2=0Ḅaz*ÐÑᑡᩩ|¥8Ḅ☢:(1)RS(2)1y((3)1☢2x—y+5z—3=0ᚖy஺":2.#☢ï(x+3ு—5)+-y—2z+4)=0,ᙠx,yv()ñ2,Ḅ☢஺"3.#RSyz+z=0*1☢ò84y882+12=0ᡂófḄ☢஺x-z+4=04":Y4-14.#RSyzᓃ==ᔁ*1P(4,l,2)Ḅ,-3Ḅ☢஺0":

295.#1☢x-2y+3z-4=0*ÐÑᑡᩩ|¥8Ḅ☢.পRS¾1,82,3¿;ফy()ñ?83ব1?1."6.È8☢1☢x+3y+2z=0kù1ᙶ᪗☢úᡂḄ<☢==û?6,#ü☢ḄPQ஺"8.yz14x+'¿,+Gz+"=°ḄÎᦪÐÑÒÓᩩ|ÔÕyzᙠᙶ᪗☢xozᑁmAX+By+Cz+D=02222"

30þ<ÿ☢ஹ┵☢ஹ☢☢§4.1☢1ஹ☢Ḅ(x-l)2+(y+3)2+(z-2)2=25>=y(஻)+YvZ=Z(H)+ZvO[ḄM,VPᦪ஺MN

31§4.2┵☢1ஹ.⚔^ᙠ_^:@@2z+l=0,y—z+l=OḄ┵☢12஺42ஹC┵☢Ḅ⚔^(3,-1,@2),@+;/—z?=i,x—y+z=O,-.fḄ12஺44ஹ.g<ᙶ᪗&"Ḅᙊ┵☢Ḅ12஺45ஹ.⚔^(1,2,4),&#☢2x+2y+z=0ᚖ(:!h;^(3,2,1)Ḅᙊ┵☢Ḅ12஺46^┵☢Ḅy(“)={x(“),y(“):z(“)},⚔^AmnḄoJ={xo:yo:z(J,-MN┵☢ḄJKOPᦪ12ᙶ᪗OPᦪ12ᑖU:/=v/(w)+(l-v)%

32X=VJC(H)+(1—v)xo'=142ஹ(=32=jxz&:./☢Ḅ12:᜛Ḅ/☢4

333ஹCḄPᦪ12x=x(“),y=yQ),z=z®),xz&:.☢ḄPᦪ12஺4᝞:§4.4ᳫ☢2221ஹ#☢X—2=0ᳫ☢4++=1ḄḄ஺429442ஹ5^^(1,0,0)Ḅ%/^ᑮ#☢x=4ḄḄ@:-.^Ḅ¡¢஺4

342223ஹ£ᳫ☢0+4+J=1Ḅ[¤¥ᓽ_^§:¨©@n1ᔣᑮ☢zḄ@^Ḅr,a"b'c5n1ᔣḄ1ᔣª«ᑖU-M:r2a2b2c2MN:¬22z4ஹᵫᳫ☢@■++¯=1Ḅ[¤:°<ᩩ±±²³ᚖ(Ḅ´:ᑖU☢஻],¶:஻3,aCஹ·…1111115OPi=4'஺஻§G:஺஻3=G:-M—HT-*=—T+7T+~rrracx23MN:5ஹ@(ᑖUᙶ᪗☢yoz,zox,my%<^A8,C,¸(¹º:(zḄ

35§4.5È☢1ஹÉgÊÈ☢Ḅ:222(1)ll-f+Ê1'(2)---—+—=-116494᝞v:2ஹÌn12=1(A>B>C>0)A-AB-AC-A-ϸXÐÑ%A,B,CḄᔜÓᦪº:f⊤ÕÖ᪵Ḅ☢?4:3ஹCᓫØÈ☢?■-5=1:-.#☢Ḅ12:Ù/#☢#$%yoz☢¥ᡈxoz☢§!☢Ḅ@Û²(஺4

364ஹ5^(4,0,0)Ḅ%/^ᑮ#☢x=lḄḄ±Ü:-./^Ḅ¡¢஺45ஹ-.ᓫØÈ☢Ý+?—]=1#☢x-2z+3=0ḄÛxoy#☢Ḅ´Þ☢஺46ஹ5(/ß³àᚖ(Ḅ±ᩩÑ☢(:C/áḄâᚖḄ[^:A,B±^ᑖUᙠ(/,ßzã:!44஺3=90",-M(ABḄ¡¢@¼ᓫØÈ☢஺MN7ஹ-æMᓫØÈ☢ÈØÈ☢ḄPᦪ12ᑖU:x=asec“cosux=atgucosvvy=0sec஻sinv

37§4.6ëᱥ☢1ஹCᙊëᱥ☢Ḅ⚔^ᙠ_^:Ûí☢XOZ☢yoz☢:!;^¥1,2,6§ï¥',-1,1§,./¼ᙊëᱥ☢Ḅ12஺42ஹ〉¸⌱Ðᙶ᪗ò:.vᑡ¡¢Ḅ12¥1§ᑮ@n^ï@n#☢óônõᦪḄ^Ḅ¡¢'¥2§±ÌnḄÑ☢(Ḅ^Ḅ¡¢:C±Ñ☢(Ḅ2஺:ᜳ÷2a஺43ஹÉvᑡ12ᡠø⊤Ḅ:,2x=y2+z2V(1)---1-——Fz=1'(2)z=xy497z=24ஹÉvᑡᔜú☢ᡠûᡂḄýþḄ¥1§y=0,z=0,3ᑍ+y=6,3x+2y=12,x+y+z=62/+=z,ᙶ᪗☢X+y=1(4)x~+y2=l,y2+z21

38:5ஹ!ᙊ#ᱥ☢%&'#ᱥ☢Ḅ)ᦪ+,-ᑖ/ᑏᡂ:x-aucosvx-a(u+v)y=businv%«y=b(u-v)12z=2uvz--uI278Ḅ9)ᦪ஺;§4.7ᓫ=&'☢%&=&'☢Ḅ>?@1ஹABᑡ>D☢Ḅ>?@E+,;1X?+y2-z2=02z=axy;2ஹABᑡ>@EᡠᡂḄ'☢78Ḅ49)ᦪx—ayz—X+2/y+4z=4A1-----==----;2<1-10[Ax-2y-4Az=4;3ஹᙠ&'#ᱥ☢Q?=zR’ATU☢3X+2i=஺Ḅ>?@஺

39:4ஹᓫ=&'☢W+q-0=1ḄXYZᩩ>?@ᙠxoy☢RḄ\]Z^_ᐸῪᙊab'cḄᑗ@஺c;5ஹA%d>@eg=2=f%2=?g=h3ijkl%☢2x+3y-5=032132-21TḄ>@Ḅmn஺;6ஹA%Bᑡᩩ>@x=l[x=-\-oZ2y+1z+25»<%-----=-----=-----y-z[y=-z-345pᐳ☢Ḅ>@ᡠ᪀ᡂḄ'☢஺;7ஹcstᓫ=&'☢ḄZ>?@Ḅuv☢Z^stwUxZE>?@ḄZᩩ>?@yzZ{|}c~v⚪%&'#ᱥ☢ḄBZ^ᡂh஺c;

408ஹAᓫ=&'☢5+-±=1Riᚖ>Ḅdᩩ>?@jḄmn+,஺9ஹc&'#ᱥ☢;•-2=2zabRḄZdᩩ>?@>jᐸjᙠZ&'r@R஺c:10ஹd☢>@Ḅ92a,ᜳ92a,t~dᩩ>@ᑖ/☢y~d☢iᚖ>A~᪵d☢j@Ḅmn஺;W'@ZḄᳮ¢§5.1W'@%>@Ḅiᐵ¤¥1.ᑏ§BᑡW'@Ḅ¨▣Aªgὡ(x,y),¬(x,y)g6(x,y).2222(1)——4-=1(2)---=1(3)y2=2px(4)x2—3y24-5x+2=0^(5)2x2-xy+y2-6x+7y-4=0.;

412.AW'@V-2xy-3y2—4x—6y+3=0%Bᑡ>@Ḅj.(1)5x—y—5=0(2)x+2y+2=0(3)x+4y-l=0(4)ᑍ-3y=0(5)2x-6y-9=0.;°±;²>@+,³ᐭ'@+,3.A>@x-y-l=0%W'@2/ZµZZ¶Z2NZ1=0Ḅj.4.·^kḄ¸¹(1)>@x—)+5=0%W'@ߟ3»+>-½=0jUd¾Ḅ¿x=1+kt(2)>@{'%W'@»2-4µ+3>2-y=0jUZ;y=k+t(3)oߟ6—1=0%W'@—2Â+:/Z(᝕—i)y—1=0jUdviÄᔠḄJQ-]+1(4){'%W'@2/+4Â+62Z=0jUdvᐳÇj.,=]+/;

42§5.2W'@ḄÈÉ+ᔣஹ8ËஹÈÉ@i.ABᑡW'@ḄÈÉ+ᔣyᢣ§'@wUÍÎÏÐḄ.(1)£+2µ+j?+3x+y=0;(2)3x2+4x^+2/-x-2j+5=0;(3)2ÓZ4x-2y+3=0.;2.ᑨÕBᑡ'@_8Ë'@ÖË'@×_@Ë'@.(1)X2—2xy+2y2-4x—6j+3=0(2)x2-4xy+4y2+2x-2y-1=0(3)2y2+8x+12y—3=0(4)9x2—6xy+y2-6x+2y=0.;3.ABᑡW'@Ḅ8Ë.(1)5x~—+3y2—2,x+3y—6=0(2)2x?++2y2—6x—3y+5=0(3)—30Â+259+8x—15y=0.:

434.ØÙÚÛÜᩩÝW'@Þ2+6µ+ᑖ2+3%+à-4=0(1)ᨵâZ8Ë(2)ãᨵ8Ë(3)ᨵZᩩ8Ë>@.;5.᝞åW'@F(x,y)=a^x1+2axy+ay2+2ax+2a^y+a=0n22ni3ᨵÈÉ@æÜçḄdvÈÉ@+,_জ(x-x,y-y)=1(x-x)2+2a(x-x)(y-y)+a22(J-^o)2=0000120078(x(>X>)9W'@Ḅ8Ë•c;6.ABᑡW'@ḄÈÉ@.(1)6x2——y2+3x+y—1=0(2)x~—3xy+2y-+x—3y+4=0(3)x2+2xy+y2+2x+2y—4=0.;7.W'@_@Ë'@Ḅᐙ⌕ᩩÝ_4=/3=0ᡂ9ÖË'@Ḅᐙ⌕ᩩÝ_/,=0,AH0.c;

448.cª>@A.x+By,+G=09ÈÉ@ḄW'@+,îïᑏᡂ(4x+8y+C])(Ax+8y+C)+£>=0.c;9.ABᑡW'@Ḅ+,.(1)ª(0,1)98Ëlòt(2,3),(4,2)%(-1,-3)(2)òt(1,1),(2,1),(-1,-2)lª>@Þ+y-l=09ÈÉ@.;ᑭᵨõ⚪8Ḅö¢§5.3W'@Ḅᑗ@1.AªBW'@ᙠᡠ÷ᡈstᡠ÷Ḅᑗ@+,.(1)'@3ᔆ+4Â+5y~—7x—8y—3=0ᙠ(2.1)(2)'@'@3/+4µ+5)2—7ûZ8üZ3=0ᙠᙠý(3)'@f+ÿ+y2+x+4y+3=0(-2,-1)(4)5f+6xy+5y2=8(0,⊈)(5)22—xy-y2_x-2y-l=0(0,2).2.!ᑡ#$Ḅᑗ'()*ᑗḄᙶ᪗.

45-1.f+4/+3y2-5x—y+3=0Ḅᑗ0123x+4y=0-2./+5+y=3Ḅᑗ0126ᙶ᪗7.83.!ᑡ#$Ḅ᜻:.(1)3X2-2/+6X+4J+1=08(2)2xy+/-2x-l=08(3)x2—2,xy+y~-2,x+2y+1=0.84.;<=ᑗ34x+3y+2=02-1,-2.>ᑗ3x-y-1=02-0,-1.Ḅ#$'(.85.?ᨵᐳᯖḄC—y^+¥^=l,FG஺IJKLMḄNᦪP012QR3a~+h~b~+h~y=mxḄḄᑗFTᑗᑗḄUV'(.8

46§5.4#$Ḅ3W1.QR#$3%2+7xy+5y2+4x+5y+l=0.ZḄ(1)[x701Ḅ\Ḅ]UV(2)[y701Ḅ\Ḅ]UV(3)[3x+y+l=O01Ḅ\Ḅ]UV.82.f+2/—4x—2y—6=0_(8,0)Ḅ3W'()ᐸᐳΊ3W.83.QR/Jbߟ2x+3y—l=0Ḅ3W[y701ZḄ'()*F3WḄᐳd3W.84.QReᱥV=-8x,_(-1,1)hJ\iZᙠFk0ᑖ.85.mn-2=1Joᐳp3WḄ'(QR6ᐳU3WqḄrI45s.64

47:6.u8_]vḄ3JwxḄ3W012yvz{'ᔣḄ3Jwxᐸ3W.u}87.!ᑡ6ᩩḄᐳ3W.(1)3%2-2y+3y2+4+ᑖ-4=0[2%2-T,xy-y2+3x+2y=0(2)x2-xy-y2-7=0[2+2+b2-+^=0.88.QR#$_<)=!ᑡ6o3x-3y-2=0,f5y+3=0,ீ'[.5x—5y—4=0[2JC—y—1=0xZḄ6oᐳ3W#$Ḅ'(.8§5.5#$Ḅ3W['ᔣ22221.ᑖᙊ5+⃩=1m*•J'=1,eᱥy2=2pxḄ'ᔣ[3W.T82.!ᑡ#$Ḅ'ᔣ[3W.

48(1)5f+8xy+5y2-1818^+9=0(2)2xy-2x+2y-1=0(3)9/-249+16J18%-101)+19=0.83.3x+y+l=OI#$Ḅ3W(0,0),(1,-1),(2,1)ᙠḄ'(.84.;u#$6ᱯ᪷wḄ'ᔣᚖ3.u}8§5.6#$'(Ḅᓄ¡[ᑖ¢1.ᑭᵨ7[¥7ᓄ¡!ᑡ#$Ḅ'()ᑏ*Z§Ḅ¨©.(1)5f+4xy+2y2-24x-12y+18=0(2)x2+2xy+/-4x+>'-l=0(3)5/+129-22%-12b-19=0(4)y2+2/+y2+2x+2y=0.82.#$Ḅ3Wx«ᙶ᪗7ᓄ¡!ᑡ'()ᑏ*Ḅᙶ᪗Lᣚ[P*Z§Ḅ¨©.(1)8x2+4jcy+5j2+8x—16j-16=0

49(2)J4/J2y2+10x+4y=0(3)4X2-4J^+/+6x-8y+3=08(4)4x2-4xy+y2+4x-2y=0.83.;uᙠ°±¥7!#$Ḅ«²'(ḄJ$⚗´ᦪµ¶ᐵ´'2'222&13+43=஽13+”13u}:3.;u#$ax2+2hxy+ay2-dḄ6ᩩ3Wxb-b=0,Ḅ6»7Ḅ¼ᑖxu}8*Ḅ63W)ᓄ¡ᓽ¾¿.

50§5.7ÀᵨLÁᓄ¡#$Ḅ'(1.ᑭᵨLÁ[»LÁᑨÃ!ᑡ#$xÄÅ)*ZḄᓄ¡'([᪗Æ'(.(1)J+6/+Ç2+6x+2y-l=0(2)3/J2/+3_/+4%+4Ç-4=0(3)f-4/+3y2+2-2y=08(4)/J4/+4yÈ+2x-2y-l=0(5)x2-2xy+2y2-4x-6y+29=0(6)\/x+y[y=4a(7)f+2/+y+2x+2y-4=0(8)4x2~^xy+y1+12x-6y+9=0.82.É;lËÄÌÍ'(Ax2+4/+b-4x-2y-3=0⊤Ï6ᩩ3.83.ᢥÑᦪ%ḄÌÒÓ'(Ax2-2xy+Ay2-2x+2y+5=0⊤ÏÔÕ.

514.?«x2+2axy+ay2+2ax+2a^+6i=0Ht222132333⊤Ï6ᩩ013u}F6ᩩ3ÈqḄÖ×Iu}:5.;u'(ax2+2axy+ay2+2ax+2ay+a=0nl222l32333wJKÑᙊØÙ=ÚÙ=4/,/,I<0.22u}86.;u᝞Ü#$ḄÝ=0,ÞÕA<0.u}87.;u᝞Ü#$Ḅ/2=0,3஺0,ÞÕHO,ß=/"2<0u}: