高数椭圆如图，那个切平面方程是怎么一下写出来的？ 高数求讲解最后一步那个切平面怎么出来的 谢谢！
\u692d\u7403\u7684\u5207\u5e73\u9762\u65b9\u7a0b\u662f\u4ec0\u4e48\uff0c\u600e\u4e48\u7528\u504f\u5bfc\u6570\u63a8\u5bfc\uff1f\u5229\u7528\u9690\u51fd\u6570\u6c42\u5bfc\uff0c\u4ee4F\uff1dx\u5e73\u65b9\uff0b2y\u5e73\u65b9\uff0b3z\u5e73\u65b9\uff0d21\uff0c\u5206\u522b\u6c42F\u5bf9x\uff0cy\uff0cz\u7684\u4e00\u9636\u504f\u5bfc\u6570\uff0c\u5f97\u5230\u7684\u5c31\u662f\u5207\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u3002
\u8fd9\u4e2a\u662f\u516c\u5f0f\uff1a
x²/a²+y²/b²+z²/c²=1\uff0c\u4e0a\u70b9\uff08x0,y0,z0\uff09\u5904\u7684\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a\uff1a
x0x/a²+y0y/b²+z0z/c²=1
\u63a8\u5bfc\u8fc7\u7a0b\uff1a
\u4ee4F(x,y,z)=x²/a²+y²/b²+z²/c²-1
Fx=2x/a²\uff0cFy=2y/b²\uff0cFz=2z/c²
n=(x0/a²\uff0cy0/b²\uff0cz0/c²)
\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a
x0/a²(x-x0)+y0/b²(y-y0)+z0/c²(z-z0)=0
\u5316\u7b80\u5373\u5f97\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u9690\u51fd\u6570\u5bfc\u6570\u7684\u6c42\u89e3\u4e00\u822c\u53ef\u4ee5\u91c7\u7528\u4ee5\u4e0b\u65b9\u6cd5\uff1a
\u65b9\u6cd5\u2460\uff1a\u5148\u628a\u9690\u51fd\u6570\u8f6c\u5316\u6210\u663e\u51fd\u6570\uff0c\u518d\u5229\u7528\u663e\u51fd\u6570\u6c42\u5bfc\u7684\u65b9\u6cd5\u6c42\u5bfc\uff1b
\u65b9\u6cd5\u2461\uff1a\u9690\u51fd\u6570\u5de6\u53f3\u4e24\u8fb9\u5bf9x\u6c42\u5bfc\uff08\u4f46\u8981\u6ce8\u610f\u628ay\u770b\u4f5cx\u7684\u51fd\u6570\uff09\uff1b
\u65b9\u6cd5\u2462\uff1a\u5229\u7528\u4e00\u9636\u5fae\u5206\u5f62\u5f0f\u4e0d\u53d8\u7684\u6027\u8d28\u5206\u522b\u5bf9x\u548cy\u6c42\u5bfc\uff0c\u518d\u901a\u8fc7\u79fb\u9879\u6c42\u5f97\u7684\u503c\uff1b
\u65b9\u6cd5\u2463\uff1a\u628an\u5143\u9690\u51fd\u6570\u770b\u4f5c(n+1)\u5143\u51fd\u6570\uff0c\u901a\u8fc7\u591a\u5143\u51fd\u6570\u7684\u504f\u5bfc\u6570\u7684\u5546\u6c42\u5f97n\u5143\u9690\u51fd\u6570\u7684\u5bfc\u6570\u3002
\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u82e5\u6b32\u6c42z = f(x,y)\u7684\u5bfc\u6570\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c06\u539f\u9690\u51fd\u6570\u901a\u8fc7\u79fb\u9879\u5316\u4e3af(x,y,z) = 0\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u901a\u8fc7\uff08\u5f0f\u4e2dF'y,F'x\u5206\u522b\u8868\u793ay\u548cx\u5bf9z\u7684\u504f\u5bfc\u6570\uff09\u6765\u6c42\u89e3\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u9690\u51fd\u6570
\u5207\u70b9\u6c42\u51fa\u6765\u4e86\uff0c\u5e26\u5165n\u6c42\u51fa\u6cd5\u5411\u91cf\uff0c\u7531\u70b9\u6cd5\u5f0f\u5c31\u53ef\u6c42\u51fa\u5e73\u9762\u65b9\u7a0b\u3002
点(x,y,z)
由点法式方程，即得切平面方程。（就是你画问好部分）
楼主，你这是什么书鸭，我也想要
切平面截距咋得出来的啊
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绛旓細鍒囧钩闈㈡柟绋搴旇涓猴細2x+4y-z=k 鍗筹細z=2x+4y-k锛屽甫鍏ユ洸闈㈡柟绋嬪緱锛2x+4y-k=x^2+y^2 (x-2)^2+(y-2)^2+(k-5)=0 姝ゆ柟绋嬫湁鍞竴涓缁勮В锛屾墍浠ワ細k-5=0锛屽嵆k=5 鎵浠ワ紝鍒囬潰鏂圭▼涓锛2x+4y-z=5
绛旓細璁惧垏鐐逛负M锛坸0锛寉0锛寊0锛夛紝鏁呮き鐞冮潰鍦ㄥ垏鐐瑰鐨鍒囧钩闈鐨勬硶鍚戦噺涓 n ={2x0锛4y0锛2z0} 锛
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绛旓細璁 f(x锛寉锛寊) = z - x^2 - y^2 锛屽垯 fx ' = -2x = -2锛宖y ' = -2y = -4锛宖z ' = 1锛屽洜姝鍒囧钩闈㈡柟绋嬩负 -2(x-1) - 4(y-2) + (z-5) = 0锛屾硶绾挎柟绋嬩负 (x-1)/-2 = (y-2)/-4 = (z-5)/1 銆
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绛旓細Fx=Fu路1+Fv路yz Fy=Fu路1+Fv路xz Fz=Fu路1+Fv路xy 鍦(1锛1锛1)澶勶紝Fx=Fy=Fz=5 鈭磏//(5锛5锛5)涓轰簡绠渚胯捣瑙侊紝鍙彇n=(1锛1锛1)鍒囧钩闈㈡柟绋嬩负 (x-1)+(y-1)+(z-1)=0 鍗筹紝x+y+z-3=0 娉曠嚎鏂圭▼涓 (x-1)/1=(y-1)/1=(z-1)/1 鍗筹紝x=y=z ...
