一道极坐标的题 不懂的地方： 1.p不是规定了取正的麽 2.cosβ不是规定0
\u4e00\u9053\u6781\u5750\u6807\u9898\u66f2\u7ebfC: \u03c1=a(1+cos\u03b8) \u5373\u5fc3\u810f\u7ebf\uff0c\u5f53\u03b8=\u03c0/2\u65f6\u5bf9\u5e94\u7684\u70b9M,\u6c42C\u5728\u70b9M\u5904\u7684\u5207\u7ebf\u65b9\u7a0b
\u89e3\uff1a\u03b8=\u03c0/2\u65f6 \u03c1=a\uff1b\u5373M\u70b9\u7684\u6781\u5750\u6807\u4e3a(a\uff0c\u03c0/2)\uff1bM\u70b9\u7684\u76f4\u89d2\u5750\u6807\u4e3a(0\uff0ca)\uff1b
\u5c06\u6781\u5de6\u8fb9\u65b9\u7a0b\u8fd8\u539f\u6210\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\uff1a\u221a(x²+y²)=a[1+x/\u221a(x²+y²)]\uff1b
\u5373\u6709x²+y²-ax=a\u221a(x²+y²);
\u8bbeF(x\uff0cy)=x²+y²-ax-a\u221a(x²+y²);
\u90a3\u4e48dy/dx=-(∂F/∂x)/(∂F/∂y)=-[2x-a-a/\u221a(x²+y²)]/[2y-a/\u221a(x²+y²)]=-[(2x-a)\u221a(x²+y²)-a]/[2y\u221a(x²+y²)-a]
\u5c06x=0\uff0cy=a\u4ee3\u5165\u5f97\u8fc7M\u70b9\u7684\u5207\u7ebf\u7684\u659c\u7387k=y'(0)=(a+1)/(2a-1)
\u6545\u8fc7\u70b9M\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3ay=[(a+1)/(2a-1)]x+a.
1.(1)\u8bbe\u70b9P\u7684\u6781\u5750\u6807\u662f\uff08\u03c1\uff0c\u03b8 \uff09\uff0c\u7531\u9898\u610fOM OP =(4/cos\u03b8)*\u03c1=12,\u5219 \u03c1=3cos\u03b8
\u6b64\u5373\u4e3a\u70b9P\u8f68\u8ff9\u65b9\u7a0b,\u5b83\u662f\u4e00\u4e2a\u5706.
\uff082\uff09R\u4e3al\u4e0a\u4efb\u610f\u4e00\u70b9\uff0cl\u4e3a\u5782\u76f4\u4e8e\u6781\u8f74\u7684\u76f4\u7ebf,\u5219RP\u7684\u6700\u5c0f\u503c\u662f1.(\u753b\u56fe\u4fbf\u77e5)
2.\u8bbe\u76f4\u7ebf\u53c2\u6570\u65b9\u7a0b:x=2+tcos\u03b1,y=tsin\u03b1.\u4ee3\u5165\u66f2\u7ebf\u65b9\u7a0b\u5f97
(2+tcos\u03b1)^2+2(tsin\u03b1)^2=1,
\u5373[(sin\u03b1)^2+1]t^2+4tcos\u03b1+3=0,
\u7531\u4e8e\u76f4\u7ebf\u4e0e\u66f2\u7ebf\u4ea4\u4e8e\u70b9M\uff0cN
\u5219(4cos\u03b1)^2-4[(sin\u03b1)^2+1]*3\u22650,\u5373(sin\u03b1)^2\u22641/7.
\u7531\u97e6\u8fbe\u5b9a\u7406\u6709
|PM|\u00b7|PN|=|t1|\u00b7|t2|=|t1\u00b7t2|=3/[(sin\u03b1)^2+1]\u226521/8
\u6545|PM|\u00b7|PN|\u7684\u6700\u5c0f\u503c\u662f 21/8\uff0c
\u6b64\u65f6 sin\u03b1=\u6839\u53f77/7\uff0c\u03b1=arcsin(\u6839\u53f77/7)\u6216\u03b1=\u03c0-arcsin(\u6839\u53f77/7).
\u4f60\u7684\u601d\u8def\u662f\u5bf9\u7684.
答案是对的
扩展阅读：θr ... 极坐标方程r cosθ ... 极坐标系rcosθ ... 经纬度开关 ... xy 1极坐标 ... 心形线1+cosx图像 ... 极坐标曲线r r θ ... 极坐标中的 为负值时 ... 极坐标系r范围的确定 ...
