1\u3001\u4e00\u822c\u5f0f
\n2\u3001\u70b9\u659c\u5f0f
\n3\u3001\u659c\u622a\u5f0f
\n4\u3001\u622a\u8ddd\u5f0f
\n5\u3001\u4e24\u70b9\u5f0f<\/p>\n
<\/p>\n
\u5bf9\u4e8e\u76f4\u7ebf<\/p>\n
$l_1:y=k_1x+b_1, \\, l_2:y=k_2x+b_2$\uff0c\u6709\uff1a<\/p>\n
\uff081\uff09$l_1 \/\/ l_2 \\Leftrightarrow \\left \\{ \\begin{array} {c} k_1 = k_2 \\ b_1 \u2260 b_2 \\end{array} \\right. $<\/p>\n
\uff082\uff09$l_1$ \u548c $l_2$ \u76f8\u4ea4 $\\Leftrightarrow k_1 \u2260 k_2$<\/p>\n
\uff083\uff09$l_1$ \u548c $l_2$ \u91cd\u5408 $\\Leftrightarrow \\left \\{ \\begin{array} {c} k_1 = k_2 \\ b_1 = b_2 \\end{array} \\right. $<\/p>\n
\uff084\uff09$l_1 \\bot l_2 \\Leftrightarrow k_1k_2 = -1$<\/p>\n
\u5bf9\u4e8e\u76f4\u7ebf<\/p>\n
$\\left. \\begin{array} {c} A_1x + B_1y + C_1 = 0 \\ A_2x + B_2y + C_2 = 0 \\end{array} \\right. $\uff0c\u6709<\/p>\n
\uff081\uff09$l_1 \/\/ l_2 \\Leftrightarrow \\left \\{ \\begin{array} {c} A_1B_2 = A_2B_1 \\ B_1C_2 \u2260 B_2C_1 \\end{array} \\right. $<\/p>\n
\uff082\uff09$l_1$ \u548c $l_2$ \u76f8\u4ea4 $\\Leftrightarrow A_1B_2 \u2260 A_2B_1$<\/p>\n
\uff083\uff09$l_1$ \u548c $l_2$ \u91cd\u5408 $\\Leftrightarrow \\left \\{ \\begin{array} {c} A_1B_2 = A_2B_1 \\ B_1C_2 = B_2C_1 \\end{array} \\right. $<\/p>\n
\uff084\uff09$l_1 \\bot l_2 \\Leftrightarrow A_1A_2 + B_1B_2 = 0$<\/p>\n
\u70b9$(x_1, y_1)$\u4e0e\u70b9$(x_2, y_2)$\u95f4\u8ddd\u79bb\uff1a<\/p>\n
$$
\nd = \\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}
\n$$<\/p>\n
\u8bbe\u70b9$P(x_0, y_0)$\uff0c\u76f4\u7ebf$ax+by+c=0$\uff0c\u70b9\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u4e3a<\/p>\n
$$
\n|PQ| = \\frac{|ax_0+by_0+c|\\sqrt{a^2+b^2}}{|ab|}
\n$$<\/p>\n
\u8bbe\u5e73\u9762\u4e0a\u4e24\u6761\u76f4\u7ebf\u65b9\u7a0b\u4e3a$Ax+By+C_1=0$\uff0c$Ax+By+C_2=0$\uff0c\u5219\u5176\u8ddd\u79bb\u516c\u5f0f<\/p>\n
$$
\nd=\\frac{|C_1-C_2|}{\\sqrt{(A^2+B^2)}}
\n$$<\/p>\n
\uff081\uff09\u6807\u51c6\u65b9\u7a0b<\/p>\n
$$
\n(x-a)^2 + (y-b)^2 = r^2
\n$$<\/p>\n
\u5176\u4e2d\u5706\u5fc3\u4e3a$(a, b)$\uff0c\u534a\u5f84\u4e3a$r$<\/p>\n
\uff082\uff09\u4e00\u822c\u65b9\u7a0b<\/p>\n
$$
\nx^2+y^2+Dx+Ey+F=0
\n$$<\/p>\n
\u5176\u4e2d\u5706\u5fc3\u4e3a$(-\\frac{D}{2}, -\\frac{E}{2})$\uff0c\u534a\u5f84\u4e3a$r=\\frac{1}{2}\\sqrt{D^2+E^2-4F}$<\/p>\n
\u76f4\u7ebf$Ax+By+C=0$\u4e0e\u5706$(x-a)^2+(y-b)^2=r^2$\u7684\u4f4d\u7f6e\u5173\u7cfb\u6709\u4e09\u79cd\uff1a<\/p>\n
$d=|O_1O_2|$<\/p>\n
(1) \u76f8\u79bb\uff1a$d>r$
\n(2) \u76f8\u5207\uff1a$d=r$
\n(3) \u76f8\u4ea4\uff1a$d<r$<\/p>\n
$d=|O_1O_2|$<\/p>\n
(1) \u5916\u79bb\uff1a$d>R+r$
\n(2) \u5916\u5207\uff1a$d=R+r$
\n(3) \u76f8\u4ea4\uff1a$R-r<d<R+r$
\n(4) \u5185\u5207\uff1a$d=R-r$
\n(5) \u5185\u542b\uff1a$d<R-r$<\/p>\n","protected":false},"excerpt":{"rendered":"
\u76f4\u7ebf\u4e0e\u70b9 1\u3001\u4e00\u822c\u5f0f 2\u3001\u70b9\u659c\u5f0f 3\u3001\u659c\u622a\u5f0f 4\u3001\u622a\u8ddd\u5f0f 5\u3001\u4e24\u70b9\u5f0f \u4e24\u6761\u76f4\u7ebf\u5e73\u884c\u3001\u76f8\u4ea4\u3001\u91cd\u5408\u3001\u5782\u76f4\u7684\u5145\u5206\u5fc5\u8981 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[509],"tags":[],"class_list":["post-2120","post","type-post","status-publish","format-standard","hentry","category-mathematics-fundamentals"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2120"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2120\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}