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English Senior High

He would say that God had given him a tail to keep the flies off, but that he would sooner have had no tail and no flies. soonerは「すぐに」って訳... Read More

2 Animal Farm pig, with a wise and benevolent appearance in spite of the fact that his tushes had never been cut. Before long the other animals began to arrive and make themselves comfortable after Jessie and Pincher, and then the pigs, who settled down in the their different fashions. First came the three dogs, Bluebell, themselves on the window-sills, the pigeons fluttered up to the straw immediately in front of the platform. The hens perched rafters, the sheep and cows lay down behind the pigs and began to chew the cud. The two cart-horses, Boxer and Clover, came in together, walking very slowly and setting down their vast hairy hoofs with great care lest there should be some small animal concealed in the straw. Clover was a stout motherly mare approaching middle life, who had never quite got her figure back after her fourth foal. Boxer was an enormous beast, nearly eighteen hands high, and as strong as any two ordinary horses put together. A white stripe down his nose gave him a somewhat stupid appearance, and in fact he was not of first- rate intelligence, but he was universally respected for his steadi- ness of character and tremendous powers of work. After the horses came Muriel, the white goat, and Benjamin the donkey. Benjamin was the oldest animal on the farm, and the worst tempered. He seldom talked, and when he did it was usually to make some cynical remark - for instance he would say that God had given him a tail to keep the flies off, but that he would sooner have had no tail and no flies. Alone animals on the farm he never laughed. If asked why, he would among the say that he saw nothing to laugh at. Nevertheless, without openly admitting it, he was devoted to Boxer; the two of them usually spent their Sundays together in the small paddock beyond the orchard, grazing side by side and never speaking. The two horses had just lain down when a brood of duck-

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Mathematics Senior High

数学2B 軌跡の問題です。 (3)で “ここで⑤よりX=-2+2/1+a^2” とありますが、なぜそうなるのでしょうか?💦

例題 114 軌跡 〔8〕・・・ 線分の中点の軌跡 (2)・・・(札 円 x2 +y2 = 1 ・・・ ① と直線 αax-y+2a=0 ・・・ ② について (2) αが (1) で求めた範囲で動くとき, その2交点を結ぶ線分の中点の座 (1)円 ①と直線 ② が異なる2点で交わるとき, αの値の範囲を求めよ。 をαを用いて表せ。 (3)(2)の中点の軌跡を求めよ。 (1) ①と直線 ② が異なる2点で交わる ① ② を連立した2次方程式 (*) の判別式DがD> 0 ①の中心と直線②の距離) (①の半径) どちらで考えるか? (2)素直に考えると・・・ X = 中点(X, aX-Y- したがっ ゆえに, (3)5 X=- よって ↑計算が繁雑 ⑥ の y 2次方程式(*)から2交点の座標を実際に求めて考える。 求めるものの言い換え 思考プロセス 2次方程式(*)の2解をα, βとする 解と係数の関係 中点のx座標 a+β 2 《ReAction 線分の中点の軌跡は,解と係数の関係を利用せよ 解 (1) ①,②より,yを消去して整理すると ⑦を Y2 = 0 よっ a a+β. ここ 2 ④よ 例題113) 軌跡 4 D>0より 3 ・④ であるから √3 例題 (1 + α²)x2 + 4ax + 4a² -1 = 0 ... ③ 94 ① ② は異なる2点で交わるから, ③の判別式をDと すると D > 0 D == (2a²)² - (1+ a²)(4a²-1) = −3a²+1 -3a²+1>0-6 円 ①の中心と直線 ② の 距離を d,円 ① の半径を r として,d<r から求 めることもできるが、(2) で交点の座標を考えるか ら,③を考える。 Play Back 8 参照 √3 Point (1) ② <a< 例題 130 (2) αが(1)で求めた範囲を動くと き,円 ①と直線②の2交点の x座標は,xの2次方程式 ③の 2つの実数解である。 3 3 1 <0 + (3 (2 (X, Y) 1 より ** ④ これらをα, β とすると,解と 係数の関係より (1) a<± としないよう -2-1a O B a+B= 4a² 1+ a2 とすると よって,円 ①と直線 ② の2交点の中点の座標を (X, Y) la+B= b a に注意する。 ■2次方程式 lax+bx+c=0の2つ の解をα,Bとすると 練習 11 198 laβ=

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