{"common":{"save":0,"post_id":"6491","level":3,"total":2,"point":50,"point_extra":0},"segment":[{"id":"7121","mon_id":"1158767","chapter_id":"1158892","post_id":"6491","question":"<p>Trong m\u1eb7t ph\u1eb3ng Oxy, kho\u1ea3ng cách t\u1eeb\u0111i\u1ec3m <span class=\"math-tex\">$M(2;0)$<\/span> \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta:sin\\alpha. x+cos\\alpha. y+2(2-sin\\alpha)=0$<\/span> b\u1eb1ng:<\/p>","options":["<strong>A. <span class=\"math-tex\">$\\sqrt{4}$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$2sin\\alpha$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$\\dfrac{2}{cos\\alpha+sin\\alpha}$<\/span><\/strong>","<strong>D. <\/strong><span class=\"math-tex\">$4$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ta có: <span class=\"math-tex\">$d(M;\\Delta)=\\dfrac{|2.sin\\alpha+0.cos\\alpha+2(2-sin\\alpha)|}{\\sqrt{sin^2\\alpha+cos^2\\alpha}}=4$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D. <\/strong><span class=\"math-tex\">$4$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:01:44","option_type":"math","len":0},{"id":"7123","mon_id":"1158767","chapter_id":"1158892","post_id":"6491","question":"<p>Kho\u1ea3ng cách t\u1eeb giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x-y+2=0$<\/span> và <span class=\"math-tex\">$x+3y-2=0$<\/span> \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta:2x+3y+4=0$<\/span><\/p>","options":["<strong>A. <span class=\"math-tex\">$2\\sqrt{10}$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$\\dfrac{3\\sqrt{13}}{5}$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$\\dfrac{5\\sqrt{13}}{13}$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$2$<\/span><\/strong>"],"correct":"3","level":"3","hint":"","answer":"<p>Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x-y+2=0$<\/span> và <span class=\"math-tex\">$x+3y-2=0$<\/span>là nghi\u1ec7m h\u1ec7 ph\u01b0\u01a1ng trình:<\/p><p><span class=\"math-tex\">$\\begin{cases}x-y+2=0\\\\x+3y-2=0\\end{cases}$<\/span> => giao \u0111i\u1ec3m I(-1; 1)<\/p><p>Kho\u1ea3ng cách t\u1eeb I (-1; 1) t\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta:2x+3y+4=0$<\/span> :<\/p><p><span class=\"math-tex\">$d(I;\\Delta)=\\dfrac{|2.(-1) +3.1+4|}{\\sqrt{2^2+3^2}}=\\dfrac{5\\sqrt{13}}{13}$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$\\dfrac{5\\sqrt{13}}{13}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:15:07","option_type":"math","len":0}]}