圆锥曲线切线方程公式 圆锥曲线切线方程
\u6c42\u5706\u9525\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\uff0c\u5207\u70b9\u5f26\u65b9\u7a0b\u7684\u516c\u5f0f\u53ca\u8bc1\u660e\u8fc7\u5e73\u9762\u4e0a\u4e00\u70b9\u5982\u679c\u53ef\u4ee5\u4f5c\u51fa\u67d0\u5706\u9525\u66f2\u7ebf\u7684\u4e24\u6761\u5207\u7ebf,\u8fde\u63a5\u4e24\u4e2a\u5207\u70b9\u5373\u4e3a\u6b64\u5706\u9525\u66f2\u7ebf\u7684\u5207\u70b9\u5f26(\u82e5\u4e3a\u53cc\u66f2\u7ebf,\u9700\u5bf9\u5176\u540c\u4e00\u652f\u4f5c\u4e24\u6761\u5207\u7ebf)\u3002\u8bbe\u70b9p(x0,y0),\u8fc7\u70b9p\u4f5c\u51fa\u7684\u5207\u7ebf\u5206...
\u8bbe\u4efb\u610f\u4e00\u70b9\u5750\u6807\u4e3a(m,n)
\u692d\u5706:
x^2/a^2+y^2/b^2=1
\u6c42\u5bfc
2x/a^2+2yy'/b^2=0
y'=-(x/y)*(b^2/a^2)
\u5207\u7ebf:
y-n=-(m/n)*(b^2/a^2)(x-m)
\u540c\u6837\u6709:
\u53cc\u66f2\u7ebf:y-n=(m/n)(b^2/a^2)(x-m)
\u629b\u7269\u7ebf:y-n=(p/n)(x-m)
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。
绛旓細鍦嗛敟鏇茬嚎鍒囩嚎鏂圭▼鍏紡鏄痻^2/a^2+y^2/b^2=1銆傚渾閿ユ洸绾垮寘鎷き鍦嗭紝鍙屾洸绾匡紝鎶涚墿绾裤1銆佹き鍦嗭細鍒颁袱涓畾鐐圭殑璺濈涔嬪拰绛変簬瀹氶暱锛堝畾闀垮ぇ浜庝袱涓畾鐐归棿鐨勮窛绂伙級鐨勫姩鐐圭殑杞ㄨ抗鍙仛妞渾銆傚嵆锛歿p| |pf1|+|pf2|=2a, (2a>|f1f2|)}銆2銆佸弻鏇茬嚎锛氬埌涓や釜瀹氱偣鐨勮窛绂荤殑宸殑缁濆鍊间负瀹氬硷紙瀹氬煎皬浜庝袱涓畾鐐...
绛旓細鍦嗛敟鏇茬嚎鍒囩嚎鏂圭▼鍏紡锛歺^2/a^2+y^2/b^2=1銆傛洸绾匡紝鏄井鍒嗗嚑浣曞鐮旂┒鐨勪富瑕佸璞′箣涓銆傜洿瑙備笂锛屾洸绾垮彲鐪嬫垚绌洪棿璐ㄧ偣杩愬姩鐨勮建杩广傚井鍒嗗嚑浣曞氨鏄埄鐢ㄥ井绉垎鏉ョ爺绌跺嚑浣曠殑瀛︾銆備负浜嗚兘澶熷簲鐢ㄥ井绉垎鐨勭煡璇嗭紝鎴戜滑涓嶈兘鑰冭檻涓鍒囨洸绾匡紝鐢氳嚦涓嶈兘鑰冭檻杩炵画鏇茬嚎锛屽洜涓鸿繛缁笉涓瀹氬彲寰傝繖灏辫鎴戜滑鑰冭檻鍙井鏇茬嚎銆傜珛浣撳嚑浣曞畾...
绛旓細鏍囧噯鏂圭▼锛(x-a)^2+(y-b)^2=r^2 (a,b)涓哄渾蹇 r涓哄崐寰 涓鑸柟绋嬶細x^2+y^2+Dx+Ey+F=0锛坉^2+e^2-4f>0 鍙傛暟鏂圭▼锛歺=a+r*cos胃,y=b+r*sin胃 (a,b)涓哄渾蹇 绔偣寮忥細(x-a1)(x-a2)+(y-b1)(y-b2)=0 (a,b)涓哄渾涓婄殑涓鐐 鍒囩嚎鏂圭▼ 锛歛0*x+b0*y=r^2 涓锛岃建杩规柟...
绛旓細1.璁鍒囩嚎鏂圭▼涓簓-1=k(x-1),浠ｅ叆鏇茬嚎鏂圭▼锛岀敤浜屾鏂圭▼鐨勫垽鍒紡=0纭畾k.2.瀵规洸绾挎柟绋嬫眰瀵硷紝锛1锛夊凡鐭ョ偣鍦ㄦ洸绾夸笂锛岀敱瀵兼暟鐨勫嚑浣曟ц川灏卞彲浠ュ啓鍑哄垏绾挎柟绋嬶紱锛2锛夊凡鐭ョ偣涓嶅湪鏇茬嚎涓婏紝鍋囪鍒囩偣涓(x0,y0),鍐欏嚭鍒囩嚎鏂圭▼锛屽啀鎶婂凡鐭ョ偣鍧愭爣浠ｅ叆銆備緥濡 鐐笰锛1,1锛変笉鍦2x^+y^=1鈶犱笂锛屽鈶犳眰瀵煎緱4x+2...
绛旓細璁句换鎰忎竴鐐瑰潗鏍囦负(m,n)妞渾:x^2/a^2+y^2/b^2=1 姹傚 2x/a^2+2yy'/b^2=0 y'=-(x/y)*(b^2/a^2)鍒囩嚎:y-n=-(m/n)*(b^2/a^2)(x-m)鍚屾牱鏈:鍙屾洸绾:y-n=(m/n)(b^2/a^2)(x-m)鎶涚墿绾:y-n=(p/n)(x-m)
绛旓細鍥炵瓟锛氫竴鑸浜屾鏇茬嚎Ax^2+Cy^2+Dx+Ey+F=0涓婁竴鐐(x`,y`),杩囪鐐圭殑鍒囩嚎鏂圭▼涓篈x`x+Cy`y+D(x`+x)/2+E(y`+y)/2+F=0
绛旓細濡傛灉涓烘爣鍑嗗紡锛歛x^2+by^2=1 瀵箈姹傚: 2ax+2byy'=0 鍗硑'=-ax/(by)鍥犳杩(x0, y0)鐨鍒囩嚎涓 y=-ax0/(by0)*(x-x0)+y0 鍖栫畝寰楀垏绾夸负锛歛x0*x+by0*y=1
绛旓細1锛夊湪妞渾涓婃湁涓鐐筆锛坸1,y1)缁忚繃姝ょ偣妞渾鐨鍒囩嚎鏂圭▼涓猴細x1*x/a^2+y1*y/b^2=1璇佹槑濡備笅锛氳鍒囩嚎鐨勬柟绋嬩负Y-Yo=k(X-Xo)鍗砓=k(X-Xo)+Yo 鈶 鎶娾憼寮忎唬鍏ユき鍦嗘柟绋媂^2/a^2+Y^2/b^2=1,寰楋細X^2/a^2+[k(X-Xo)+Yo]^2/b^2=1鍗筹細b^2路X^2+a^2路[k^2路(X-Xo)^2+Yo^...
绛旓細浠绘剰涓鏉鍦嗛敟鏇茬嚎锛屽叾涓袱鏉＄浉浜ょ殑鍒囩嚎鐨勬枩鐜囦箣绉负瀹氬笺 杩欎釜缁撹鍙互鐢ㄥ涓嬫柟娉曡瘉鏄庯細 鍋囪鍦嗛敟鏇茬嚎涓婃湁涓や釜浜ょ偣A銆丅锛屼袱鏉″垏绾跨殑鏂滅巼鍒嗗埆涓簁1銆乲2銆傚湪杩欎袱涓氦鐐瑰锛屽垏绾跨殑鏂圭▼鍒嗗埆涓簓=k1x+b1鍜寉=k2x+b2銆
绛旓細濡傛灉宸茬煡鍦嗛敟鏇茬嚎鏂圭▼涓篺(rou, theta) = 0锛屾眰鐩磋鍧愭爣绯讳笅鍒囩嚎鏂滅巼锛岄偅涔堜唬鍏ワ細rou = sqrt (x^2 + y^2)锛宼heta = arc tan (y/x)锛屽氨鏈 f( sqrt (x^2 + y^2) , arc tan (y/x)) = 0 锛屼袱杈瑰悓鏃跺x姹傚锛屾敞鎰忚繖閲寉宸茬粡鏄痻鐨勯殣鍑芥暟浜嗭紝y^2鐨勫鏁颁负2yy'銆傝В鍑簓'鍗冲彲銆傚鏋...
