已知抛物线y＝x2－6x＋8与x轴交于A，B两点，与y轴交于点C，求过点A.B.C的圆M的方程 如图，已知二次函数y=a（x 2 -6x+8）(a>0...
\u5df2\u77e5\u629b\u7269\u7ebfy=x²-6x+8\u4e0ex\u8f74\u4ea4\u4e8eA,B\u4e24\u70b9\uff0c\u4e0ey\u8f74\u4ea4\u4e8e\u70b9C\uff0cy=x^2-6x+8=(x-2)*(x-4)
A(2,0),B(4,0),C(0,8)
AC=\u221a68,AB=\u221a80,AB=2
(1)
L=
(2)
s=(1/2)*(4-2)*8=8
(1) A\uff082\uff0c0\uff09\uff0cB\uff084\uff0c0\uff09;(2) D\uff086\uff0c8\uff09\uff1b\uff083\uff09 \uff0c\u4e0d\u5b58\u5728\uff0e \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u4ee4y=0\uff0c\u5219x 2 -6x+8=0\uff0c\u89e3\u5f97\uff1ax 1 =2\uff0cx 2 =4\uff0c\u2234A\uff082\uff0c0\uff09\uff0cB\uff084\uff0c0\uff09\uff082\uff09\u2235S \u25b3ABC = AB\u00b7OC= \u00d72\u00d78a=8\uff0c\u2234a=1\uff0cC(0\uff0c8)\u2235\u629b\u7269\u7ebf\u4e0e\u5706\u5747\u4e3a\u8f74\u5bf9\u79f0\u56fe\u5f62\uff0c\u90fd\u5173\u4e8e\u76f4\u7ebfx=3\u5bf9\u79f0\uff0c\u2234\u5706\u4e0e\u629b\u7269\u7ebf\u7b2c\u56db\u4e2a\u4ea4\u70b9\u4e3aD\uff086\uff0c8\uff09\uff083\uff09\u2460\u5c06\u25b3OAC\u6cbf\u76f4\u7ebfAC\u7ffb\u6298\uff0c\u70b9O\u7684\u5bf9\u5e94\u70b9O\u2032\u843d\u5728\u5bf9\u79f0\u8f74x=3\u4e0a\uff0c\u2234AE=1\uff0cAO="2" \u5728Rt O\u2032AE\u4e2d\uff0c\u2220O\u2032AM=60\u00b0\u2234\u2220CAO=60\u00b0 \u2234a= \u2461\u8fc7A\u70b9\u4f5cAF\u22a5BC\uff0cE\u4e3a\u5782\u8db3\uff0c\u2234AF=2\uff1cAB\uff0c\u5373AF\uff1cOA\u2234\u4e0d\u8bbaa\u53d6\u4f55\u503c\uff0cO\u70b9\u7684\u5bf9\u5e94\u70b9O\u2032\u603b\u843d\u5728\u25b3ABC\u7684\u5916\u90e8\u2234\u8fd9\u6837\u7684\u6574\u6570a\u4e0d\u5b58\u5728\uff0e
解：与x轴相交时，y=0.即x^2-6x+8=0,解得x1=2，x2=4.A(2,0),B（4，0）；与y轴相交时，x=0.即y=8，C(0，8）.圆M过三点，将坐标代入（x-a）^2+(y-b)^2=r^2得：（2-a）^2+b^2=r^2,(4-a)^2+b^2=r^2,a^2+(8-b)^2=r^2,得：a=3，b=4.5，r^2=21.25.M为（x-3)^2+(y-4.5)^2=21.25先求交点，(2，0)，(4，0)和(0，8)
绛旓細瑙ｏ細涓巟杞寸浉浜ゆ椂锛y=0.鍗硏^2-6x+8=0,瑙ｅ緱x1=2锛x2=4.A(2,0),B锛4锛0锛夛紱涓巠杞寸浉浜ゆ椂锛寈=0.鍗硑=8锛孋(0锛8锛.鍦哅杩囦笁鐐癸紝灏嗗潗鏍囦唬鍏ワ紙x-a锛塣2+(y-b)^2=r^2寰楋細锛2-a锛塣2+b^2=r^2,(4-a)^2+b^2=r^2,a^2+(8-b)^2=r^2,寰楋細a=3锛宐=4.5锛宺^2=...
绛旓細鎶涚墿绾鏀瑰啓涓涓 y=(x-2)(x-4) A B 涓ょ偣鐨勫潗鏍囦负 锛2锛0锛 锛4锛0锛夈愭敞鎰忎笉鏄搴斿叧绯汇慍鐐逛负 锛0锛8锛夆柍ABC鐨勯潰绉 浠B涓哄簳 楂樺氨鏄 C鐨勭旱鍧愭爣缁濆鍊煎槢 0.5*锛4-2锛*8=8骞虫柟鍗曚綅 鈻矨BC鐨勫懆闀 鐢ㄤ袱涓嬀鑲″畾鐞 姹傚埌涓や釜鏂滆竟 AC BC涔嬮暱鍐嶅姞涓夾B涔嬮暱 涓2+4鈭5+2...
绛旓細鎶妝=0浠ｅ叆y=x2-6x+8寰梮2-6x+8=0锛岃В寰梮1=2锛寈2=4锛屾墍浠鎶涚墿绾涓巟杞寸殑浜ょ偣鍧愭爣涓猴紙2锛0锛夊拰锛4锛0锛夛紱锛2锛墆=x2-6x+8=锛坸-3锛2-1锛屾墍浠ユ姏鐗╃嚎鐨勯《鐐瑰潗鏍囦负锛3锛-1锛夛紱锛3锛夊綋x锛2鎴杧锛4鏃讹紝鍑芥暟鍊煎ぇ浜0锛
绛旓細1)x=0鏃讹紝y=8, 鍗充笌y杞翠氦浜(0,8)y=0鏃讹紝瑙ｆ柟绋媥^2-6x+8=0, 寰楋細(x-2)(x-4)=0, 寰楋細x=2, 4.鏁呬笌x杞翠氦鐐逛负(2,0),(4,0)2)y=(x-3)^2-1, 鏁呴《鐐逛负(3, -1)3)褰搙>4鎴杧<2鏃讹紝y>0 4)瀵圭О杞翠负x=3,寮鍙ｅ悜涓婏紝鏁厁<=3鏃讹紝y闅弜鐨勫澶ц屽噺灏忋
绛旓細-6x+8=锛坸-3)²-1 鍗鎶涚墿绾鐨勯《鐐瑰潗鏍囷紙3锛-1锛2浠y=0 鍗硏²-6x+8=0 鍗筹紙x-2锛夛紙x-4锛=0 鍒橝(2,0),B(4,0)鐢眡=0锛寉=8.鍗矯锛0锛8锛夊垯鈻砤bc=1/2/AB//OC/=1/2*2*8=8 3 鍒欌憽x锛2鎴杧锛4鏃讹紝鍑芥暟鍊煎ぇ浜0鈶2锛渪锛4鏃讹紝鍑芥暟鐨勫煎皬浜0銆
绛旓細,涓嶻杞存湁涓涓氦鐐:(0,8)鈶″嚱鏁y=x^2-6x+8,鏄鎶涚墿绾,鍥爔^2鍓嶇殑绯绘暟鏄1澶т簬0,鎵浠,鍑芥暟鏈夋渶灏忓.鍥犱负褰搙=3鏃,鏄姏鐗╃嚎鐨勫绉拌酱,鎵浠ユ渶灏忓兼槸褰搙=3鏃,瑙ｅ緱y=-1,鎵浠,褰搙>-1鏃,y闅忕潃x鐨勫澶ц屽澶.浠=0鏃,鍙В寰梮=2,x=4,鍥犱负鎶涚墿绾垮紑鍙ｅ悜涓,鎵浠,褰搙<2鎴杧>4鏃,y>0....
绛旓細宸茬煡鎶涚墿绾縴=x2+6x+8锛屽寲涓轰袱鐐瑰紡涓簓=锛坸+2锛夛紙x+4锛夊緱鍑簒1=-2锛寈2=-4锛庡張鍥犱负鐐筂锛-1锛0锛夋槸鍦嗗績锛1涓哄崐寰勶紝鐢诲浘鍙緱鎶涚墿绾夸笌鈯橫鏈変袱涓氦鐐癸紟
绛旓細(1)y=(x-2)(x-4)鐭ヤ笌x杞翠氦鐐瑰潗鏍囧垎鍒槸(2,0)(4,0)浠=0寰椾笌y杞村潗鏍囨槸(0锛8锛(2)瀵圭О杞磝=3 宸茬粡涓婅堪涓巟 y杞翠氦鐐瑰潗鏍囷紝鏍规嵁鎻忕偣娉曪紝鍗冲彲寰楀嚱鏁板浘鍍 (3)鏂圭▼鐨勮В鍗充负鍥惧儚涓巟杞寸殑浜ょ偣妯潗鏍 鏍规嵁绗竴闂紝鍙煡鏂圭▼鐨勮В涓簒=2 x=4 ...
绛旓細瑙ｏ細鐢y=a(x²-6x+8)锛屼护y=0寰楋紝x²-6x+8=0锛寈1=2锛x2=4锛屼护x=0寰椼y=8a锛岄厤鏂瑰緱y=a(x-3)²-a锛屼簬鏄緱a鈮0锛孉(2锛0)锛孊(4,0)锛孋(0锛8a)锛孌(3锛-a)(2)璇佹槑锛氬洜涓篜鐐瑰湪EF涓婏紝鏁呭彲璁綪(4锛宐)锛屽垯3鈮鈮4 PA²=(4-2)²+b²...
绛旓細(1)浠y=x²-6x+8=0锛屽嵆(x-2)(x-4)=0锛屸埓x=2锛屾垨x=4锛屸埓涓巟杞寸殑浜ょ偣涓(2,0)鍜(4,0)浠=0锛岄偅涔坹=x²-6x+8=8锛屸埓涓巠杞寸殑浜ょ偣涓(0,8)(2)y=x²-6x+8=(x-3)²-1锛屸埓椤剁偣鍧愭爣涓(3,-1)(3)浠=x²-6x+8=(x-2)(x-4)<0锛屸埓2<x...
