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HomeLớp 10Toán lớp 10 - Sách Kết nối tri thứcBài 21. Đường tròn trong mặt phẳng tọa độBài tập trung bình
{"common":{"save":0,"post_id":"6490","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7097","mon_id":"1158767","chapter_id":"1158892","post_id":"6490","question":"<p>Trong m\u1eb7t ph\u1eb3ng v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy, cho \u0111\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+2y-4=0$<\/span>. Vi\u1ebft ph\u01b0\u01a1ng trình ti\u1ebfp tuy\u1ebfn d c\u1ee7a \u0111\u01b0\u1eddng tròn (C), bi\u1ebft ti\u1ebfp tuy\u1ebfn \u0111ó song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta:3x-4y-5=0$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$3x-4y-5=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y+25=0$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$3x-4y+5=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-25=0$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$3x-4y-5=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-25=0$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$3x-4y-5=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x+4y+25=0$<\/span><\/strong>"],"correct":"2","level":"2","hint":"","answer":"<p>\u0110\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+2y-4=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow (x-2)^2+(y+1)^2=9$<\/span> nên có tâm <span class=\"math-tex\">$I(2;-1)$<\/span> và bán kính <span class=\"math-tex\">$R=3$<\/span>.<\/p><p>Vì ti\u1ebfp tuy\u1ebfn d c\u1ee7a \u0111\u01b0\u1eddng tròn (C) song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta:3x-4y-5=0$<\/span> nên <span class=\"math-tex\">$d:3x-4y+k=0\\space(k\\ne5)$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$d(I,d)=\\dfrac{|3.2+4.1+k|}{\\sqrt{3^2+4^2}}=3$<\/span> <span class=\"math-tex\">$\\Leftrightarrow|10+k|=15$<\/span> <span class=\"math-tex\">$\\Leftrightarrow 10+k=15$<\/span> ho\u1eb7c <span class=\"math-tex\">$10+k=-15$<\/span> <span class=\"math-tex\">$\\Leftrightarrow k=5$<\/span> ho\u1eb7c <span class=\"math-tex\">$k=-25$<\/span>.<\/p><p>V\u1eady có hai ph\u01b0\u01a1ng trình ti\u1ebfp tuy\u1ebfn c\u1ea7n tìm là<strong> <span class=\"math-tex\">$3x-4y+5=0$<\/span><\/strong> và <strong><span class=\"math-tex\">$3x-4y-25=0$<\/span>.<\/strong><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <span class=\"math-tex\">$3x-4y+5=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-25=0$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-02 08:54:40","option_type":"math","len":0},{"id":"7101","mon_id":"1158767","chapter_id":"1158892","post_id":"6490","question":"<p>Vi\u1ebft ph\u01b0\u01a1ng trình ti\u1ebfp tuy\u1ebfn <span class=\"math-tex\">$\\Delta$<\/span> c\u1ee7a \u0111\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+8y-5=0$<\/span>, bi\u1ebft ti\u1ebfp tuy\u1ebfn <span class=\"math-tex\">$\\Delta$<\/span> vuông góc v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:4x+3y+2=0$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$3x-4y-35=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-47=0$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$3x-4y+3=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-15=0$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$3x-4y+3=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-47=0$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$3x-4y-3=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y+47=0$<\/span><\/strong>"],"correct":"3","level":"2","hint":"","answer":"<p>\u0110\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+8y-5=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow (x-2)^2+(y+4)^2=25$<\/span> nên có tâm <span class=\"math-tex\">$I(2;-4)$<\/span> và bán kính <span class=\"math-tex\">$R=5$<\/span>.<\/p><p>Vì ti\u1ebfp tuy\u1ebfn <span class=\"math-tex\">$\\Delta$<\/span> c\u1ee7a \u0111\u01b0\u1eddng tròn (C) vuông góc v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:4x+3y+2=0$<\/span> nên <span class=\"math-tex\">$\\Delta:3x-4y+k=0$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$d(I,\\Delta)=\\dfrac{|3.2+4.4+k|}{\\sqrt{3^2+4^2}}=5$<\/span> <span class=\"math-tex\">$\\Leftrightarrow|22+k|=25$<\/span> <span class=\"math-tex\">$\\Leftrightarrow 22+k=25$<\/span> ho\u1eb7c <span class=\"math-tex\">$22+k=-25$<\/span> <span class=\"math-tex\">$\\Leftrightarrow k=3$<\/span> ho\u1eb7c <span class=\"math-tex\">$k=-47$<\/span>.<\/p><p>V\u1eady có hai ph\u01b0\u01a1ng trình ti\u1ebfp tuy\u1ebfn c\u1ea7n tìm là<strong> <span class=\"math-tex\">$3x-4y+3=0$<\/span><\/strong> và <strong><span class=\"math-tex\">$3x-4y-47=0$<\/span>.<\/strong><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$3x-4y+3=0$<\/span><\/strong>; <strong><span class=\"math-tex\">$3x-4y-47=0$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-02 09:17:43","option_type":"math","len":0},{"id":"7102","mon_id":"1158767","chapter_id":"1158892","post_id":"6490","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho \u0111\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+8y-5=0$<\/span>. T\u1eeb \u0111i\u1ec3m <span class=\"math-tex\">$A(1;1)$<\/span> k\u1ebb \u0111\u01b0\u1ee3c bao nhiêu ti\u1ebfp tuy\u1ebfn \u0111\u1ebfn \u0111\u01b0\u1eddng tròn (C)?<\/p>","options":["<strong>A. <\/strong>1","<strong>B. <\/strong>2","<strong>C. <\/strong>Vô s\u1ed1","<strong>D. <\/strong>0"],"correct":"2","level":"2","hint":"","answer":"<p>\u0110\u01b0\u1eddng tròn <span class=\"math-tex\">$(C):x^2+y^2-4x+8y-5=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow (x-2)^2+(y+4)^2=25$<\/span> nên có tâm <span class=\"math-tex\">$I(2;-4)$<\/span> và bán kính <span class=\"math-tex\">$R=5$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$IA=\\sqrt{(1-2)^2+(1+4)^2}=\\sqrt{26}>R$<\/span> nên A n\u1eb1m bên ngoài \u0111\u01b0\u1eddng tròn (C).<\/p><p>Do \u0111ó t\u1eeb A k\u1ebb \u0111\u01b0\u1ee3c <strong>2 <\/strong>ti\u1ebfp tuy\u1ebfn \u0111\u1ebfn \u0111\u01b0\u1eddng tròn.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <\/strong>2<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-02 09:24:55","option_type":"txt","len":1}]}