求到定点F(c,0)与到定直线l:x=a^2/c距离之比是c/a(c/a>1)的点M的轨迹
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![求到定点F(c,0)与到定直线l:x=a^2/c距离之比是c/a(c/a>1)的点M的轨迹](/uploads/image/z/10776278-38-8.jpg?t=%E6%B1%82%E5%88%B0%E5%AE%9A%E7%82%B9F%EF%BC%88c%2C0%29%E4%B8%8E%E5%88%B0%E5%AE%9A%E7%9B%B4%E7%BA%BFl%3Ax%3Da%5E2%2Fc%E8%B7%9D%E7%A6%BB%E4%B9%8B%E6%AF%94%E6%98%AFc%2Fa%28c%2Fa%3E1%29%E7%9A%84%E7%82%B9M%E7%9A%84%E8%BD%A8%E8%BF%B9)
求到定点F(c,0)与到定直线l:x=a^2/c距离之比是c/a(c/a>1)的点M的轨迹
求到定点F(c,0)与到定直线l:x=a^2/c距离之比是c/a(c/a>1)的点M的轨迹
求到定点F(c,0)与到定直线l:x=a^2/c距离之比是c/a(c/a>1)的点M的轨迹
设M(x,y),c/a>1 c>a
MF=√[(x-c)^2+y^2],点M到直线L的距离=[x-a^2/c]
√[(x-c)^2+y^2]/[x-a^2/c]=c/a [(x-c)^2+y^2]/(x-a^2/c)^2=c^2/a^2
x^2-2cx+c^2+y^2=(c^2/a^2)(x^2-2a^2x/c+a^4/c^2)=c^2x^2/a^2-2cx+a^2
x^2+c^2+y^2=c^2x^2/a^2+a^2 a^2x^2+a^2c^2+a^2y^2=c^2x^2+a^4
(c^2-a^2)x^2-a^y^2=a^2(c^2-a^2) 设c^2-a^2=b^2
b^2x^2-a^2y^2=a^2b^2 两边同除a^2b^2
x^2/a^2-y^2/b^2=1