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 ...