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Part2 47 Example 161 93 1 T a a 2 M 1 a 1 T a 2 a Point 1 T L L L T T L L T L L L T T L L T detm a 1 aa 2 a 1 2 + 1 > 0 11 T T x x M λ 12 y y x y λ 2 a + 1λ + a 2 2a + 2 0 13 D D a + 1 2 4a 2 2a + 2 a 13a 7 14 a < 1 7 3 < a 0 a 1 a 7 3 1 < a < 7 3 1 2 15 a < 1 7 3 < a ; a 1 ; x α 1 1 α α t 0 1 t t t 16 16 x α x α y mx + n 1 1 t 1 mt n 0 1 mt + n mt + n t 17

Part2 48 17 y mx + n mt + n m 1 mt n + n t m 2 t + mn 0 t m 0 n 18 y n n a 7 3 ; x α 1 7 1 α 1 7α +t 3 4 3 t 3 4α + 3t t 19 19 x α x α y mx + n 1 7 1 t 1 m + 7t + n 3 4 3 mt + n 3 3m 4t + 3n 110 y mx + n 1 3 3m 4t + n m 1 3 m + 7t + m 1 3 n + n t y 2x t 110 m + 2 2 t + mn 0 t m 2 n 0 111 1 < a < 7 3 ; x α a a 2 α aα + a 2t 1 a 1 t 1 aα +t t 112 a 2 α 0 x 0 y mx + n a a 2 t a + a 2mt + a 2n 1 a 1 mt + n 1 at + mt + n 113 y mx + n 1 a + mt + n ma + a 2mt + a 2mn + n t 114 a 2 t 113 a 2m 2 + a 1m + a 1 t + a 2mn 0 t 114 m + 1t 0 t m 1 n 115 y x + n n 114 a 2 a 2m 2 + a 1m + a 1 0 116 116 D D a 1 2 4a 1a 2 a 13a 7 > 0 1 < a < 7 3 117

Part2 49 116 m a 1 ± a 13a 7 2a 2 118 118 m y mx 2 2 116 m 1 m 2 m 1 m 2 a 1 a 2 1 a 3 2 119 2 y 1 ± 5 x 120 2 a < 1 7 < a 3 0 a 1 y c c a 2 y x + c c x 0 1 a 7 3 y 2x 1 1 < a < 7 3 a 2 y a 1 ± a 13a 7 x 2a 2 esp a 3 y 1 ± 5 x 2 2 2 2 Review 1611 88 1 T 1 1 0 1 y x + 1 T [ ] y x + c c Review 1612 92 k + 1 1 1 k k k 1 [ ] k < 1 0 k 1 k 1 ± 5 1 2 k > 1 k 0 k 3 k 1 ± 5 2 2 k 0 k 3

Part2 50 1 T x x M y y x 0 M E a 1 b x c d 1 y 0 0 { a 1x + by 0 cx + d 1y 0 1 x y 0 0 x y 0 0 1 detm E 0 detm tracem 1 0 M 1 1 x 0 1 { a 1 + b 0 b d 1 t t t 0 2 cx 0 + d 1 0 a 1 c 2 2 b a 1 d 1 c 2 P O OP t t 0 T OP M t t M P T P t λ 1 x 0 M λe 0 0 a λ b c d λ { a λ + b 0 cx 0 + d λ 0 0 0 OP 3 b d λ t t t 0 4 a λ c 4 OP t t 0 T OP M t t M tλ λ OP λ 1 5!! M λ 1 λ 2

Part2 51 λ j 0 λ j 1 j 1 2 M λ j E x j 0 x j y j 0 y j b t t a λ j d λ j t 0 j 1 2 6 c λ 1 λ 2 { a λ1 x + by 0 7 cx + d λ 1 y 0 8 { a λ2 x + by 0 9 cx + d λ 2 y 0 10 7 8 9 10 bc 0 2 a λ 1 x + by 0 cx + d λ 1 y 0 7 8 11 a λ 2 x + by 0 cx + d λ 2 y 0 9 10 λ 1 λ 2 λ 0 1 a λ 0 x + by 0 cx + d λ 0 y 0 12 b 0 c 0 a + d λ 1 + λ 2 ad λ 1 λ 2 a d λ 1 λ 2 a d λ 2 λ 1 13 a d λ 1 λ 2 2 { cx + d ay 0 8 x 0 9 10 14 a d λ 2 λ 1 2 { cx + d ay 0 10 x 0 7 8 15 λ 1 λ 2 λ 0 1 x 0 8 10 a d λ0 16 b 0 c 0 13 a d λ 1 λ 2 λ 2 λ 1 a d λ 1 λ 2 2 { a dx + by 0 9 y 0 7 8 17 a d λ 2 λ 1 2 { a dx + by 0 7 y 0 9 10 18 λ 1 λ 2 λ 0 1 y 0 7 9 a d λ0 19

Part2 52 b c 0 13 a d λ 1 λ 2 λ 2 λ 1 a d λ 1 λ 2 2 { x 0 9 y 0 8 20 a d λ 2 λ 1 2 { x 0 7 y 0 10 21 λ 1 λ 2 λ 0 M λ 0 E a d λ 0 0 1

Part2 53 λ 1 1 λ 2 1 λ 2 0 6 λ 1 1 λ 2 { a 1x + by 0 22 cx + d 1y 0 23 { a λ2 x + by 0 24 cx + d λ 2 y 0 25 λ2 1 λ 2 0 22 23 24 25 bc 0 22 23 x 0 0 0 x2 OP +t t : 26 y 2 26 P Q OQ T x2 x2 OP M +t M +tλ 2 27 y 2 y 2 x 0 0 0 x 2 y 2 26 a 1x + by 0 cx + d 1y 0 22 23 a λ 2 x + by + r 0 cx + d λ 2 y + r 0 24 25 28 r : b 0 c 0 a + d 1 + λ 2 ad 1 λ 2 a d 1 λ 2 a d λ 2 1 29 a d 1 λ 2 { cx + d 1y 0 23 x r 24 25 r : 30 a d λ 2 1 { cx + 1 ay + r 0 25 r : x 0 22 23 31 b 0 c 0 29 a d 1 λ 2 λ 2 1 a d 1 λ 2 { 1 dx + by + r 0 24 r : y 0 22 23 32 a d λ 2 1 { a 1x + by 0 22 y r 24 25 r : 33

Part2 54 b c 0 29 a d 1 λ 2 λ 2 1 a d 1 λ 2 { y 0 23 x r 24 r : a d λ 2 1 { x 0 22 y r 25 r : 34 35

Part2 55 λ 1 λ 2 1 6 λ 1 λ 2 1 { a 1x + by 0 36 cx + d 1y 0 37 36 37 bc 0 36 37 x 0 put Q R QR OR OQ M M E a 1 b a 1 b c d 1 1 a 12 1 a b 38 a 1x 0 + b b b a 1 38 a + d λ 1 + λ 2 2 ad bc λ 1 λ 2 1 d 2 a c 1 b a 12 b 0 39 36 b a 1 1 b QR // a 1x 0 + b 0 40 a 1 b a 1x + by + r 0 cx + d 1y + r 0 r 0 41 a 1x + by 0 cx + d 1y 0 36 37 a 1x + by + r 0 cx + d 1y + r 0 36 37 42 r : b 0 c 0 a + d λ 1 + λ 2 2 ad λ 1 λ 2 1 a d 1 43 { x 0 37 x r 41 b 0 c 0 43 a d 1 { y 0 36 y r 41 b c 0 43 a d 1 M E r : r : 44 45

Part2 56 Example 1621 1 T A B C T A B T B C T C A 211 ABC G G O Point 1 T s t T s u +t v st u +t T v u v 1 211 T 1{ OG T OA + T OB + T 3 } 1 OC 3 OB + OC + OA OG 212 T OG OG T G G 213 G 3 A B C GA GB CG 1 s t u 214 T GO s GA +t GB + ugc s +t + u 1 214 T GO st GA +t T GB + ut GC GO s GB +t GC + u GA 215 215 T T GO st GB +t T GC + ut GA GO s GC +t GA + u GB 216 214 215 216 3 GO s +t + u GA + GB + GC 1 0 G O 217 OG 1 OA + OB + OC GA + GB + GC 0 218 3

Part2 57 Example 1622 1 T P L T T L L Q T P T OP OP 221 T λ T λ OP λ T OP λ OP 222 2 O P g g 1 L g ; L g Q Q g T OQ OQ T Q Q 223 Q L 223 T L L T L L g Q 2 L g ; L // g ; L d g d λ OP T d T λ OP λ T OP λ OP d T d d 224 T d T L 224 L // T L 225 L T L Q P L T L Q g L Q P T L O s _ Ì W

Part2 58 Comment 1 Review 1621 xy O OAB 1 T T A B T B B P Q 1 Q OB 2 P OB PQ // AB [ ] Review 1622 1 T 1 u v T u v T v λ u T λ [ ] λ > 0 2 λ 0 1 λ < 0 0 Review 1623 90 2 C C 1 T C C T T 1 L C P L T L T P C A C T A C [ ]

Part2 59 Example 163 92 xy 2 x 2 + 2axy + y 2 + 2x 8y + b 0 31 θ x 2 3 y2 5 1 32 a b θ 0 θ π 2 1 a M a 1 33 2 31 5x 2 3y 2 15 0 32 M λ 1 5 λ 2 3 34 { tracem λ1 + λ 2 5 + 3 2 detm detm λ 1 λ 2 5 3 15 35 1 a 2 15 a ±4 36 a 4 ; λ 1 λ 2 1 v1 1 v2 1 1 M P P 1 1 1 cos45 sin45 2 1 1 sin45 cos45 θ θ π 4 < 0 37 38 39 a 4 ; λ 1 λ 2 1 v1 1 v2 1 1 M P P 1 1 1 cos 45 sin 45 2 1 1 sin 45 cos 45 θ 0 < θ π 4 < π 2 31 π/4 32 b 14 a 4 b 14 θ π 4 310 311 312 313

Part2 60 Comment ax 2 + 2bxy + cy 2 + px + qy + r 0 314 a b p x M N X t N p q t X x y 315 b c q y t XMX + t NX + r 0 316 M 2 t P P 1 t P P P t P E detp 1 317 P X P X X PX X P 1 X 318 t X P 1 MP X + t NP X + r 0 319 t X x y λ 1 x 2 + λ 2 y 2 + p x + q y + r 0 320 p q t NP [Note] P 317 t P P E detp 1 [Review 1532] Point ax 2 + 2bxy + cy 2 + px + qy + r 0 detm > 0 detm 0 detm < 0

Part2 61 Review 1631 95 2 C : x 2 2xy + y 2 2x + 3 2y 0 1 C y ax 2 + bx + c a > 0 2 C x + 2y + 6 2 0 [ ] 1 a 1 b 2 c 0 2 343 6 Review 1632 96 2 C : 9x 2 + 2 3xy + 7y 2 60 1 C ax 2 + by 2 1 2 C c 3c 2 c > 0 [ ] 1 a 1 10 b 1 6 2 c 1 3 2 + 10 2

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