圆锥曲线切线方程公式 求圆锥曲线的计算公式，还有简便的公式
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\u7acb\u4f53\u51e0\u4f55\u5b9a\u4e49\uff1a\u4ee5\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u76f4\u89d2\u8fb9\u6240\u5728\u76f4\u7ebf\u4e3a\u65cb\u8f6c\u8f74\uff0c\u5176\u4f59\u4e24\u8fb9\u65cb\u8f6c360\u5ea6\u800c\u6210\u7684\u66f2\u9762\u6240\u56f4\u6210\u7684\u51e0\u4f55\u4f53\u53eb\u505a\u5706\u9525\u3002\u65cb\u8f6c\u8f74\u53eb\u505a\u5706\u9525\u7684\u8f74\u3002\u5782\u76f4\u4e8e\u8f74\u7684\u8fb9\u65cb\u8f6c\u800c\u6210\u7684\u66f2\u9762\u53eb\u505a\u5706\u9525\u7684\u5e95\u9762\u3002
\u4e00\u3001\u5706
[\u5706\u7684\u65b9\u7a0b\u3001\u5706\u5fc3\u4e0e\u534a\u5f84]
\u65b9\u7a0bx²+ y²= R²
\u5706\u5fc3\u4e0e\u534a\u5f84
\u5706\u5fc3 G(0,0)
\u534a\u5f84 r = R
(x -a)²+(y - b)²= R²
\u5706\u5fc3 G(a, b)
\u534a\u5f84 r = R
x²+y²+2mx + 2ny + q = 0
m²+ n²> q
\u5706\u5fc3 G(-m,-n)
\u534a\u5f84
r2-2rr0cos(j-j0)+r02 = R2 (\u6781\u5750\u6807\u65b9\u7a0b)
\u5706\u5fc3 G(r0,j0)
\u534a\u5f84 r = R
x2 + y2 = 2Rx
\u6216r= 2Rcosj
(\u6781\u5750\u6807\u65b9\u7a0b)
\u5706\u5fc3 G(R, 0)
\u534a\u5f84 r = R
[\u5706\u7684\u5207\u7ebf]
\u5706 x²+ y²= R²\u4e0a\u4e00\u70b9M(x0, y0)\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a
x0x + y0y = R²
\u5706 x2 + y2 + 2mx + 2ny + q = 0 \u4e0a\u4e00\u70b9M(x0, y0)\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a
x0x + y0y + m(x + x0) + n(y + y0) + q = 0
[\u4e24\u4e2a\u5706\u7684\u4ea4\u89d2\u3001\u5706\u675f\u4e0e\u6839\u8f74]
\u65b9\u7a0b\u4e0e\u56fe\u5f62
\u516c\u5f0f\u4e0e\u8bf4\u660e
\u4e24\u4e2a\u5706\u7684\u4ea4\u89d2
C1 x²+y²+2m1x +2n1y +q1 = 0
C2 x²+y²+2m2x +2n2y +q2 = 0
\u4e24\u4e2a\u5706\u7684\u4ea4\u89d2\u662f\u6307\u5b83\u4eec\u5728\u4ea4\u70b9\u7684\u4e24\u6761\u5207\u7ebf\u7684\u5939\u89d2
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\u4e24\u4e2a\u5706C1\u548cC2\u6b63\u4ea4\u6761\u4ef6\u4e3a
2m1m2 + 2n1n2 - q1 - q2 = 0
\u5706\u675f\u00d7 \u4e24\u4e2a\u5706\u7684\u6839\u8f74
C1+ lC2 = 0 (l\u4e3a\u53c2\u6570)
\u6216 (l+1)(x2+y2) +2(m1+lm2)x
+(n1+ln2)y + (q1 +lq2) = 0
\u6839\u8f74\u65b9\u7a0b\u4e3a2(m1 - m2)x + 2(n1 - n2)y + (q1 - q2) = 0
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(a)\u5982\u679cC1\u548cC2\u76f8\u4ea4\u4e8e\u4e24\u70b9M1\uff0cM2\uff0c\u5219\u675f\u4e2d\u4e00\u5207\u5706\u90fd\u901a\u8fc7\u4e24\u4ea4\u70b9M1\uff0cM2\uff0c\u5b83\u4eec\u7684\u6839\u8f74\u5c31\u662f\u5b83\u4eec\u7684\u516c\u5171\u5f26.\u8fd9\u65f6\u5706\u675f\u79f0\u4e3a\u5171\u8f74\u5706\u7cfb(\u56fe(a)).
(b)\u5982\u679cC1\u548cC2\u5207\u4e8e\u4e00\u70b9M\uff0c\u5219\u675f\u4e2d\u4e00\u5207\u5706\u90fd\u5728\u4e00\u70b9M\u76f8\u5207\uff0c\u6839\u8f74\u5c31\u662f\u5728\u70b9M\u7684\u516c\u5207\u7ebf(\u56fe(b)).
(c)\u5982\u679cC1\u548cC2\u4e0d\u76f8\u4ea4\uff0c\u5219\u675f\u4e2d\u4e00\u5207\u5706\u90fd\u4e0d\u76f8\u4ea4\uff0c\u6839\u8f74\u4e5f\u4e0e\u5706\u675f\u4e2d\u4e00\u5207\u5706\u90fd\u4e0d\u76f8\u4ea4(\u56fe(c)).
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\uff08i\uff09O, M, M¢\u5171\u7ebf\uff0c
\uff08ii\uff09OM\u00d7 OM¢= r2\uff0c
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\u53cd\u6f14\u5177\u6709\u6027\u8d28\uff1a
1\u00b0 \u4e0d\u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u4e00\u6761\u76f4\u7ebf\u53d8\u4e3a\u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u4e00\u4e2a\u5706.
2\u00b0 \u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u5706\u53d8\u4e3a\u4e0d\u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u76f4\u7ebf.
3\u00b0 \u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u4e00\u6761\u76f4\u7ebf\u53d8\u4e3a\u5b83\u81ea\u5df1.
4\u00b0 \u4e0d\u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u5706\u53d8\u4e3a\u4e0d\u901a\u8fc7\u53cd\u6f14\u4e2d\u5fc3\u7684\u5706.
5\u00b0 \u53cd\u6f14\u5706\u53d8\u4e3a\u5b83\u81ea\u5df1.
6\u00b0 \u4e0e\u53cd\u6f14\u5706\u6b63\u4ea4\u7684\u5706\u53d8\u4e3a\u5b83\u81ea\u5df1\uff0c\u5176\u9006\u4e5f\u771f.
7\u00b0 \u5982\u679c\u4e24\u6761\u66f2\u7ebfC1\uff0cC2\u4ea4\u4e8e\u4e00\u70b9M\uff0c\u5219\u7ecf\u8fc7\u53cd\u6f14\u540e\u7684\u66f2\u7ebfC1¢, C2¢\u5fc5\u4ea4\u4e8eM\u7684\u53cd\u6f14\u70b9M¢.
8\u00b0 \u5982\u679c\u4e24\u6761\u66f2\u7ebfC1, C2\u5728\u4e00\u70b9M\u76f8\u5207\uff0c\u5219\u7ecf\u8fc7\u53cd\u6f14\u540e\u7684\u66f2\u7ebfC1¢, C2¢\u5fc5\u5728M\u7684\u53cd\u6f14\u70b9M¢\u76f8\u5207.
9\u00b0 \u4e24\u6761\u66f2\u7ebf\u7684\u4ea4\u89d2\u5728\u53cd\u6f14\u4e0b\u662f\u4e0d\u53d8\u7684.\u7531\u6b64\u53ef\u89c1\uff0c\u53cd\u6f14\u662f\u4e00\u4e2a\u4fdd\u89d2\u53d8\u6362\u3002
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[\u66f2\u7387\u534a\u5f84]R
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[\u5f27\u957f]=
\u5f0f\u4e2de\u4e3a\u79bb\u5fc3\u7387
[\u9762\u79ef] S
\u5f13\u5f62(AMN)\u7684\u9762\u79ef\uff1a
OAMI\u7684\u9762\u79ef\uff1a
\u8fd9\u91ccOI, OJ\u4e3a\u6e10\u8fd1\u7ebf\uff0cMI // OJ
圆锥曲线切线方程公式是x^2/a^2+y^2/b^2=1。
圆锥曲线包括椭圆，双曲线，抛物线。
1、椭圆：到两个定点的距离之和等于定长（定长大于两个定点间的距离）的动点的轨迹叫做椭圆。即：{p| |pf1|+|pf2|=2a, (2a>|f1f2|)}。
2、双曲线：到两个定点的距离的差的绝对值为定值（定值小于两个定点的距离）的动点轨迹叫做双曲线。即{p|||pf1|-|pf2||=2a, (2a<|f1f2|)}。
3、抛物线：到一个定点和一条定直线的距离相等的动点轨迹叫做抛物线。
4、圆锥曲线的统一定义：到定点的距离与到定直线的距离的比e是常数的点的轨迹叫做圆锥曲线。当0<1时为椭圆：当e=1时为抛物线；当e>1时为双曲线。
立体几何定义：以直角三角形的直角边所在直线为旋转轴，其余两边旋转360度而成的曲面所围成的几何体叫做圆锥。旋转轴叫做圆锥的轴。垂直于轴的边旋转而成的曲面叫做圆锥的底面。
绛旓細澶у鏁板涓撲笟瑙ｆ瀽鍑犱綍鍐呭銆傝繃鍦嗛敟鏇茬嚎ax^2+bxy+cy^2+dx+ey+f=0涓婁竴鐐筆(x0锛寉0)鐨鍒囩嚎鏂圭▼鍏紡锛歛x0x+b(x0y+y0x)/2+cy0y+d(x+x0)/2+e(y+y0)/2+f=0 鍦嗗ソ鍔烇紝鍏朵綑涓嶅ソ鍔烇紝涓婇潰鐨勬帹瀵肩涓涓紝鍏朵綑绫讳技锛歬(OP)=y0/x0锛宬(鍒囩嚎)=-x0/y0 鐐瑰垏寮忓垏绾挎柟绋嬶細y-y0=(-x0/y0...
绛旓細褰鍦嗛敟鏇茬嚎涓哄渾褰㈡椂 鐩寸嚎涓庡渾鍒囦簬鐐筽锛坸0銆.y0锛夊垯 鐩寸嚎鏂圭▼ 锛坸0-a锛夛紙x-a锛+锛坹0-b锛夛紙y-b锛=r^2 ...妞渾锛屽弻鏇茬嚎涔熻繖鏍 褰撶洿绾胯繘杩噋锛坸0锛寉0锛夋眰鍒囩嚎 璁惧垏鐐癸紙x1锛寉1锛夛紙x1-a锛塣2+锛坹1-b锛塣2=r^2 涓斻傦紙x0-a锛夛紙x1-a锛+锛坹0-b锛夛紙y1-b锛=r^2 姹傚嚭鐩寸嚎鏂圭▼ 鎴...
绛旓細鎯宠薄涓涓嬶紝褰撴垜浠皢鍦嗙疆浜庤繖涓簭鍒椾腑锛屼緥濡傚渾浠ョ偣锛坸0, y0锛変负涓績锛屾眰杩囪繖涓壒瀹氱偣鐨勫垏绾裤傚綋鍒囩嚎鐨勬枩鐜囧瓨鍦ㄦ椂锛屾垜浠彲浠ラ氳繃鍦嗙殑鍗婂緞鍜屽垏鐐圭殑鍧愭爣鏉ヨ绠楋紝鐢鍏紡(y - y0) = m(x - x0)锛屽叾涓璵鏄垏绾跨殑鏂滅巼銆傛荤粨鏉ヨ锛鍒囩嚎鏂圭▼涓鍦嗛敟鏇茬嚎鐨勫師鏂圭▼涔嬮棿骞堕潪鍋剁劧鐨勫阀鍚堬紝鑰屾槸鍑犱綍涓栫晫閲屼竴閬撶編濡...
绛旓細濡傛灉宸茬煡鍦嗛敟鏇茬嚎鏂圭▼涓篺(rou, theta) = 0,姹傜洿瑙掑潗鏍囩郴涓鍒囩嚎鏂滅巼,閭ｄ箞浠ｅ叆锛歳ou = sqrt (x^2 + y^2),theta = arc tan (y/x),灏辨湁f( sqrt (x^2 + y^2) , arc tan (y/x)) = 0 ,涓よ竟鍚屾椂瀵箈姹傚,娉ㄦ剰杩欓噷y宸茬粡鏄痻鐨勯殣...
绛旓細鍙屾洸绾匡細P鍦ㄥ乏鏀紝|PF1|=锛峚-ex |PF2|=a-ex P鍦ㄥ彸鏀紝|PF1|=a+ex |PF2|=锛峚+ex P鍦ㄤ笅鏀紝|PF1|= 锛峚-ey |PF2|=a-ey P鍦ㄤ笂鏀紝|PF1|= a+ey |PF2|=锛峚+ey 鍦嗛敟鏇茬嚎鐨鍒囩嚎鏂圭▼锛氬渾閿ユ洸绾夸笂涓鐐筆锛坸0,y0锛夌殑鍒囩嚎鏂圭▼浠0x浠ｆ浛x^2,浠0y浠ｆ浛y^2;浠(x0+x)/2...
绛旓細鍦 x2 + y2 + 2mx + 2ny + q = 0 涓婁竴鐐筂(x0, y0)鐨鍒囩嚎鏂圭▼涓 x0x + y0y + m(x + x0) + n(y + y0) + q = 0 [涓や釜鍦嗙殑浜よ銆佸渾鏉熶笌鏍硅酱]鏂圭▼涓庡浘褰 鍏紡涓庤鏄 涓や釜鍦嗙殑浜よ C1 x²+y²+2m1x +2n1y +q1 = 0 C2 x²+y...
绛旓細闂涓锛鍦嗛敟鏇茬嚎鍒板ぇ瀛︽墠鐭ラ亾鐨勫嚑浣曟ц川鏈夐偅浜涳紵 鍒椾笂涓浜 甯﹁瘉鏄庢洿璋㈣阿浜 鐜板湪楂樹腑鍑洪鍩烘湰涓婇兘鏄ぇ瀛 楂樿冩簮浜庢暀鏉愶紝蹇呴』鐣ラ珮浜庢暀鏉愩傛湰浜虹粨鍚堝巻骞撮珮鑰冪紪钁椾竴鏈婇珮鑰冨父鑰冪殑澶т竴鏁板銆嬫湁鍏冲渾閿ユ洸绾跨殑鏈夊洓绾夸竴鏂圭▼銆1銆 鑻锛坸0,y0锛夊湪妞渾x2锛廰2+y2锛廱2=1涓婏紝寰楀埌鍒囩嚎鏂圭▼涓 x0x锛廰2+y0y...
绛旓細鍦嗛敟鏇茬嚎鍏紡锛氭き鍦 1銆佷腑蹇冨湪鍘熺偣锛岀劍鐐瑰湪x杞翠笂鐨勬き鍦嗘爣鍑鏂圭▼锛氬叾涓瓁²/a²+y²/b²=1,鍏朵腑a>b>0,c²=a²-b²2銆佷腑蹇冨湪鍘熺偣锛岀劍鐐瑰湪y杞翠笂鐨勬き鍦嗘爣鍑嗘柟绋嬶細y²/a²+x²/b²=1,鍏朵腑a>b>0,c²=a²-b²鍙傛暟鏂圭▼...
绛旓細=x0^2+Dx0+y0^2+Ey0+F 鎵浠ュ垏绾緼B闀=鈭(x0^2+Dx0+y0^2+Ey0+F)鐢ㄥ嬀鑲″畾鐞嗘樉鐒跺彲寰桝B闀=鈭歔(x0-A)^2+(y0-B)^2-r^2]鍒囩嚎鏂圭▼鏄爺绌跺垏绾夸互鍙婂垏绾跨殑鏂滅巼鏂圭▼锛屾秹鍙婂嚑浣曘佷唬鏁般佺墿鐞嗗悜閲忋侀噺瀛愬姏瀛︾瓑鍐呭銆傛槸鍏充簬鍑犱綍鍥惧舰鐨勫垏绾垮潗鏍囧悜閲忓叧绯荤殑鐮旂┒銆傚垎鏋愭柟娉曟湁鍚戦噺娉曞拰瑙ｆ瀽娉曘
绛旓細x^2=2Py 姹傚 2x=2Py'y'=x/P 鎵浠ュ湪x^2=2Py涓婁换鎰忎竴鐐(x0,y0)鐨勫垏绾挎枩鐜囨槸x0/P 鎵浠鍒囩嚎鏂圭▼鏄(y-y0)/(x-x0)=x0/P x^2+y^2=r^2 y=鏍瑰彿涓(r^2-x^2)鎴杫=-鏍瑰彿涓(r^2-x^2)姹傚 y'=-x/鏍瑰彿涓(r^2-x^2),鎴杫=x/鏍瑰彿涓(r^2-x^2)鎵浠ュ垏绾挎槸(y-y0)/(x-...
