一圆锥面的顶点在(0,0,a),轴为z轴,半顶角为45度则它的方程是？ 求顶点为M(0,4,0)并与球面x^2+y^2+z^2=4相...
\u6c42\u4ee5\u4e09\u5750\u6807\u4e3a\u6bcd\u7ebf\u7684\u5706\u9525\u9762\u7684\u65b9\u7a0b\u3002\u8be6\u7ec6\uff0c\u8c22\u8c22\u3002xy+yz+zx=0\uff0c\u6216xy+yz-zx=0\uff0c\u6216xy-yz+zx=0\uff0c\u6216xy-yz-zx=0
\u4ee5\uff080.0.0\uff09\u4e3a\u5706\u9525\u9762\u9876\u70b9\uff081.0.0\uff09(0.1.0)(0.0.1)\u5728\u5706\u9525\u4e0a\uff0c\u7531\u4e09\u70b9\u51b3\u5b9a\u7684\u5e73\u9762x+y+z=1\u4e0e\u7403\u9762x^2+y^2+z^2=1\u7684\u4ea4\u7ebfl\u662f\u5706\u9525\u9762\u51c6\u7ebf\u3002
\u8bbe\u70b9p(x\uff0cy\uff0cz)\u662f\u5706\u9525\u9762\u4e0a\u7684\u70b9\uff0c\uff08u\uff0cv\uff0cw\uff09\u662f\u5706\u9525\u9762\u6bcd\u7ebfop\u4e0el\u7684\u4ea4\u70b9\uff0c\u5219op\u7684\u65b9\u7a0b\u4e3ax/u=y/v=z/w=1/t\uff0c\u5373u=xt\uff0cv=yt\uff0cw=zt
\u5e26\u5165\u51c6\u7ebf\u65b9\u7a0b\uff0c\u5f97\u65b9\u7a0b\u7ec4\uff08x+y+z\uff09t=1\u548c\uff08x^2+y^2+z^2\uff09t^2=1
\u6d88\u9664t\uff0c\u5f97\u5230\u5706\u9525\u9762\u65b9\u7a0bxy+yz+zx=0
\u6269\u5c55\u8d44\u6599\uff1a
\u5782\u76f4\u4e8e\u8f74\u7684\u8fb9\u65cb\u8f6c\u800c\u6210\u7684\u66f2\u9762\u53eb\u505a\u5706\u9525\u7684\u5e95\u9762\u3002\u4e0d\u5782\u76f4\u4e8e\u8f74\u7684\u8fb9\u65cb\u8f6c\u800c\u6210\u7684\u66f2\u9762\u53eb\u505a\u5706\u9525\u7684\u4fa7\u9762\u3002\u65e0\u8bba\u65cb\u8f6c\u5230\u4ec0\u4e48\u4f4d\u7f6e\uff0c\u4e0d\u5782\u76f4\u4e8e\u8f74\u7684\u8fb9\u90fd\u53eb\u505a\u5706\u9525\u7684\u6bcd\u7ebf\u3002
\u6bcd\u7ebf\u957f\u7b49\u4e8e\u5e95\u9762\u5706\u76f4\u5f84\u7684\u5706\u9525\uff0c\u5c55\u5f00\u7684\u6247\u5f62\u5c31\u662f\u534a\u5706\u3002\u6240\u6709\u5706\u9525\u5c55\u5f00\u7684\u6247\u5f62\u89d2\u5ea6\u7b49\u4e8e\uff08\u5e95\u9762\u76f4\u5f84\u00f7\u6bcd\u7ebf\uff09\u00d7180\u5ea6\u3002
\u5706 \u53c2\u6570\u65b9\u7a0b\uff1ax=X+rcos\u03b8 y=Y+rsin\u03b8 \u5706\u5fc3\u5750\u6807\uff08X,Y)
\u692d\u5706 \u53c2\u6570\u65b9\u7a0b\uff1ax=acos\u03b8 y=bsin\u03b8 a>b\u65f6\u7126\u70b9\u5728x\u8f74\u4e0a\uff0c\u53cd\u4e4b\u5728 y\u8f74\u4e0a
\u53cc\u66f2\u7ebf \u53c2\u6570\u65b9\u7a0b\uff1ax=asec\u03b8 y=btan\u03b8 \u7126\u70b9\u5728\u5e73\u884cx\u8f74\u7684\u76f4\u7ebf\u4e0a\uff08\u5c31\u662fx2\u2215a2-y2\u2215b2=1\uff09
\u7126\u70b9\u5728\u5e73\u884cy\u8f74\u7684\u76f4\u7ebf\u4e0a\uff08\u5373y2\u2215a2-x2\u2215b2=1\uff09\uff0c\u628a\u6b63\u5207\u548c\u6b63\u5272\u4ea4\u6362
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u5706\u9525
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u5706\u9525\u66f2\u7ebf\u6807\u51c6\u65b9\u7a0b
\u4e0d\u80fd\u753b\u56fe\uff0c\u5c3d\u91cf\u6587\u5b57\u8868\u8ff0\u6e05\u695a
\u5706\u9525\u9762\u4e0e\u7403\u76f8\u5207\uff0c\u5219\u7403\u5fc3\u4e00\u5b9a\u5728\u5706\u9525\u4e2d\u8f74\u7ebf\u4e0a\uff0c\u53ef\u89c1\u4e2d\u8f74\u7ebf\u5373x=z=0
\u5706\u9525\u4e0a\u7684\u70b9\u6ee1\u8db3\uff1a\u5411\u4e2d\u8f74\u7ebf\u4f5c\u5782\u7ebf\uff0c\u5782\u7ebf\u957f\u4e0e\u5782\u8db3\u548c\u9876\u70b9\u7684\u8ddd\u79bb\u4e4b\u6bd4\u662f\u5b9a\u503c\uff0c\u90fd\u7b49\u4e8e\u5706\u9525\u9876\u89d2\u7684\u4e00\u534a\u7684\u6b63\u5207\u3002
\u56e0\u6b64\u53ef\u5f97\u5f85\u5b9a\u7cfb\u6570\u65b9\u7a0b\uff1ak(4-y)^2=(x^2+z^2)
\u7531\u4e8e\u548c\u534a\u5f84\u4e3a2\u7684\u7403\u76f8\u5207\uff0c\u5219\u4f5c\u5706\u9525\u4e0a\u4efb\u610f\u4e00\u5207\u70b9\u7684\u6bcd\u7ebf\uff0c\u518d\u7403\u4e0a\u4f5c\u51fa\u8fc7\u5207\u70b9\u7684\u534a\u5f84\uff0c\u4e24\u8005\u5e94\u5f53\u5782\u76f4\u3002\u56e0\u6b64\uff0c\u534a\u9876\u89d2\u7684\u6b63\u5f26=\u534a\u5f84/\u7403\u5fc3\u548c\u9876\u70b9\u8ddd\u79bb=1/2
\u6240\u4ee5\u534a\u9876\u89d230\u00b0\uff0ck\u4e3a\u6b63\u5207\u7684\u5e73\u65b9\uff0c\u4e3a1/3
\u6240\u4ee5\u65b9\u7a0b\uff1a(4-y)^2=3x^2+3z^2
∵半顶角为45°
∴顶点到截面的距离丨z-a丨为这个圆的半径
∴这个圆锥面方程为
x²+y²=(z-a)²
一一一一一一
满意，请及时采纳。谢谢！
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