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数学 高校生

数学の図形と方程式についての質問です。水色マーカーを引いたところなのですが、xy≠0とは具体的にxとyがどのような値のときのことを指しているのでしょうか。また、(2)でX二乗 +Y二乗≠0なので…とありますが、なぜX=Y=0を除くのでしょうか?

208 第3章 図形と方程式 Think 例題 107 反転による軌跡 **** 原点を端点とする半直線上の2点P(x, y), Q(X, Y) が OP・OQ=4 を 満たしている. (1) x, y を X,Yで表せ. (2)点Pが直線2x+y=1上を動くとき,点Qの軌跡を求めよ. [考え方 点Pは半直線OQ上にあるから, OP:OQ=t:1(t>0) とおける my 3点 O P Q は, 0 t<1 のとき, 0.P.Qの順に,t>1の とき 0 QPの順に並ぶ. 解答 また,OP=√x+y0Q=√X+Yであり,xy=0のとき x と X,y と Yは同符号より OP:OQ=x: X=y: Y である. Y .8) A メー (1)点Pは半直線OQ上にあるから, OP:OQ=t: 1 (t>0) とおける. OP=tOQ であり,OP=√xty, OQ=√X2+Y2 より, OP:OQ=tOQ=t(X2+Y2) OP・OQ=4 より t(X2+ Y2)=4 これより X2+Y20 であるから, t= X2+12 xy=0 のとき,x と X, y と Yは同符号より, OP: OQ=x: X=y: Y=t: 1 (t>0) x Xx 解 Comment <反転と 定点 半直線 点Qを対 反転の中 〈円や直 (I) 反 (II) 反 (Ⅲ) P (IV) 円や 題である がこの した。 4X したがって,x=tX より ① を代入して, x= 2 X2+Y2 同様にして, 4Y y=ty=- X2+Y2 ......③ x=0 のとき, X=0 より ② に含まれ, y=0 のときも同様に③に含まれる。 (証明 010 を 4X 4Y よって, x= X+y2, y= X2+Y2 Xb (2) 2x+y=1 に② ③ を代入すると, 2. 4XX 4Y + X2+Y2 X2+Y2 =1 ○とか 8X +4Y = X2+Y2 より, (X-4)+(Y-2)=20 0=Y. ただし,X+Y=0 より X=Y=0 を除く. よって、点Qの軌跡は, (0)M 0=8+X+- 【X' + Y' = 0 となるのは, |X=Y=0 のとき (9-0)0-+ 練習 中心 (4, 2), 半径2√50円 ただし, 原点を除く. 注〉定点0を端点とする半直線上の2点P Q について, OP・OQ=k (kは定数k>0) の 関係で点 Q を点Pに対応させる(これを「反転」 とよぶ) と,円が直線に変換されたり, 直線が円に変換されるなど,これまでにない図形の対応関係が生まれる. (次ページ解 説を参照)封 原点を端点とする半直線上の2点P(x, y), Q(X, Y) が OP・OQ=1 を減 [107] たしている. ****(1)点Pが原点を通る直線 ax+by=0 上を動くとき,点Qの軌跡を求め。 (2)P (x+1)^2+(y-2)=5 上を動くとき,点Qの軌跡を求めよ。 (3)点Pが原点を通らない円(x-a)+(y-b)=r上を動くとき,点Qの 跡を求めよ. ただし, r>0 とする。 反 は

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英語 高校生

英語の長文です どこに文法表現があるか知りたいです! よろしくお願いします。

5 UNIT3 Reading Passage 10 15 20 20 25 30 Listening When important events are happening around the world, most people turn to traditional media sources, such as CNN and BBC,¹ for their news. However, during the invasion of Iraq by the United States and its allies in early 2003, a significant number of people followed the war from the point of view of an anonymous² Iraqi citizen who called himself "Salam Pax" (salam means "peace" in Arabic, and pax means "peace" in Latin). Salam Pax wrote a diary about everyday life in Baghdad during the war, and posted it on his web site. Pax's online diary was a kind of web site known as a "blog." Blogs, short for "web-logs," are online diaries usually kept by individuals, but sometimes they are written by companies and other groups of people. They are a rapidly growing type of web site on the Internet. There are estimated to be several hundred thousand blogs on the Internet, and with the popularity of other social media sites, the number of people writing online about their lives continues to grow. may find A blog differs from a traditional web site in several ways. Most importantly, it is updated much more regularly. Many blogs are updated every day, and some are updated several times a day. Also, most blogs use special software or web sites which are specifically aimed at bloggers, so you do not need to be a computer expert to create your own blog. This means that ordinary people who computers difficult to use can easily set up and start writing their own blog. In 2003, the Internet company AOL³ introduced their own blogging service, enabling its 35 million members to quickly and easily start blogging. There are many different kinds of blogs. The most popular type is an online diary of links, where the blog writer surfs the Internet and then posts links to sites or news articles that they find interesting, with a few comments about each one. Other types are personal diaries, where the writer talks about their life and feelings. Sometimes these blogs can be very personal. There is another kind of blogging, called "moblogging," short for "mobile blogging." Mobloggers use cell phones to take photo's, which are posted instantly to the Internet. When the content and images posted online involve news subjects, mobloggers become citizen journalists. In fact, the Korean web site OhMyNews was a well known source for articles from international citizen journalists. However, in 2010, OhMyNews stopped posting new articles. Instead, it is now a blog site where citizen journalists can choose what makes the headlines, or just share ideas about how regular people are changing the news world. Anyone who visits the web site of a big media company can clearly see how the idea of blogging has changed the reporting of news. Quite often, a list of reader comments follow news articles. It seems that the news is becoming less like a report or a lecture, and more like a conversation, where anyone can join in. CNN, BBC Cable News Network, British Broadcasting Corporation anonymous not named; unknown 3 AOL America Online

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英語 高校生

関係詞の分野です。至急解答をお願いします🙏

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