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HomeLớp 10Toán lớp 10 - Sách Kết nối tri thứcBài 21. Đường tròn trong mặt phẳng tọa độBài tập cơ bản
{"common":{"save":0,"post_id":"6488","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7070","mon_id":"1158767","chapter_id":"1158892","post_id":"6488","question":"<p>Trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy, tìm t\u1ecda \u0111\u1ed9 tâm I c\u1ee7a \u0111\u01b0\u1eddng tròn \u0111i qua ba \u0111i\u1ec3m <span class=\"math-tex\">$A(0;-1),B(1;-2),C(2;0)$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$I\\bigg(\\dfrac{-7}{6};\\dfrac{5}{6}\\bigg)$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$I\\bigg(\\dfrac{-7}{6};\\dfrac{2}{3}\\bigg)$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$I\\bigg(\\dfrac{7}{6};\\dfrac{-5}{6}\\bigg)$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$I\\bigg(\\dfrac{7}{6};\\dfrac{5}{6}\\bigg)$<\/span><\/strong>"],"correct":"3","level":"1","hint":"","answer":"<p>Gi\u1ea3 s\u1eed ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng tròn \u0111i qua 3 \u0111i\u1ec3m A, B, C có d\u1ea1ng <span class=\"math-tex\">$(C):x^2+y^2+2ax+2by+c=0$<\/span>.<\/p><p>Thay t\u1ecda \u0111\u1ed9 <span class=\"math-tex\">$A(0;-1),B(1;-2),C(2;0)$<\/span> ta \u0111\u01b0\u1ee3c:<\/p><p><span class=\"math-tex\">$\\begin{cases}1-2b+c=0\\\\5+2a-4b+c=0\\\\4+4a+c=0\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=2b-1\\\\2a-4b+c=-5\\\\c=-4-4a\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=2b-1\\\\a-b=-2\\\\4a+2b=-3\\end{cases} \\Leftrightarrow$<\/span><span class=\"math-tex\">$\\begin{cases}a=\\dfrac{-7}{6}\\\\b=\\dfrac{5}{6}\\\\c=\\dfrac{2}{3}\\end{cases} $<\/span><\/p><p>Suy ra tâm \u0111\u01b0\u1eddng tròn là <strong><span class=\"math-tex\">$I\\bigg(\\dfrac{7}{6};\\dfrac{-5}{6}\\bigg)$<\/span><\/strong><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$I\\bigg(\\dfrac{7}{6};\\dfrac{-5}{6}\\bigg)$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 09:28:57","option_type":"math","len":0},{"id":"7073","mon_id":"1158767","chapter_id":"1158892","post_id":"6488","question":"<p>Trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy, tìm bán kính c\u1ee7a \u0111\u01b0\u1eddng tròn \u0111i qua ba \u0111i\u1ec3m <span class=\"math-tex\">$A(0;-1),B(1;-2),C(2;0)$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$\\dfrac{5}{6}$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$\\dfrac{\\sqrt{2}}{18}$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$\\dfrac{5\\sqrt{2}}{6}$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$\\dfrac{25}{18}$<\/span><\/strong>"],"correct":"3","level":"1","hint":"","answer":"<p>Gi\u1ea3 s\u1eed ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng tròn \u0111i qua 3 \u0111i\u1ec3m A, B, C có d\u1ea1ng <span class=\"math-tex\">$(C):x^2+y^2+2ax+2by+c=0$<\/span>.<\/p><p>Thay t\u1ecda \u0111\u1ed9 <span class=\"math-tex\">$A(0;-1),B(1;-2),C(2;0)$<\/span> ta \u0111\u01b0\u1ee3c:<\/p><p><span class=\"math-tex\">$\\begin{cases}1-2b+c=0\\\\5+2a-4b+c=0\\\\4+4a+c=0\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=2b-1\\\\2a-4b+c=-5\\\\c=-4-4a\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=2b-1\\\\a-b=-2\\\\4a+2b=-3\\end{cases} \\Leftrightarrow$<\/span><span class=\"math-tex\">$\\begin{cases}a=\\dfrac{-7}{6}\\\\b=\\dfrac{5}{6}\\\\c=\\dfrac{2}{3}\\end{cases} $<\/span><\/p><p>Suy ra bán kính \u0111\u01b0\u1eddng tròn là <span class=\"math-tex\">$R=\\sqrt{\\dfrac{49}{36}+\\dfrac{25}{36}-\\dfrac{2}{3}}=\\dfrac{5\\sqrt{2}}{6}$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$\\dfrac{5\\sqrt{2}}{6}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 10:00:45","option_type":"math","len":0},{"id":"7077","mon_id":"1158767","chapter_id":"1158892","post_id":"6488","question":"<p>Trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy, cho <span class=\"math-tex\">$A(0;4),B(2;4),C(2;0)$<\/span>. Vi\u1ebft ph\u01b0\u01a1ng trình c\u1ee7a \u0111\u01b0\u1eddng tròn ngo\u1ea1i ti\u1ebfp tam giác ABC.<\/p>","options":["<strong>A. <span class=\"math-tex\">$(C):x^2+y^2-2x-4y=0$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$(C):x^2+y^2-2x-4y-2=0$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$(C):x^2+y^2-2x-4y-4=0$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$(C):x^2+y^2-2x+4y=0$<\/span><\/strong>"],"correct":"1","level":"1","hint":"","answer":"<p>Gi\u1ea3 s\u1eed ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng tròn \u0111i qua 3 \u0111i\u1ec3m A, B, C có d\u1ea1ng <span class=\"math-tex\">$(C):x^2+y^2+2ax+2by+c=0$<\/span>.<\/p><p>Thay t\u1ecda \u0111\u1ed9 <span class=\"math-tex\">$A(0;4),B(2;4),C(2;0)$<\/span> ta \u0111\u01b0\u1ee3c:<\/p><p><span class=\"math-tex\">$\\begin{cases}8b+c=-16\\\\4a+8b+c=-20\\\\4a+c=-4\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=-8b-16\\\\2a-4b+c=-5\\\\c=-4-4a\\end{cases} \\Leftrightarrow$<\/span> <span class=\"math-tex\">$\\begin{cases}c=-8b-16\\\\4a=-4\\\\8b=-16\\end{cases} \\Leftrightarrow$<\/span><span class=\"math-tex\">$\\begin{cases}a=-1\\\\b=-2\\\\c=0\\end{cases} $<\/span><\/p><p>Suy ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng tròn \u0111i qua 3 \u0111i\u1ec3m A, B, C là <span class=\"math-tex\">$(C):x^2+y^2-2x-4y=0$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A. <span class=\"math-tex\">$(C):x^2+y^2-2x-4y=0$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 10:17:57","option_type":"math","len":0}]}