椭圆x^2/a^2+y^2/b^2=1,(a>b>0); 右焦点为F,直线l方程为x=a2/c,求证椭圆上任意点P到F的距离与到l的距离之比为c/a
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![椭圆x^2/a^2+y^2/b^2=1,(a>b>0); 右焦点为F,直线l方程为x=a2/c,求证椭圆上任意点P到F的距离与到l的距离之比为c/a](/uploads/image/z/14675044-4-4.jpg?t=%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%2C%28a%3Eb%3E0%29%3B+%E5%8F%B3%E7%84%A6%E7%82%B9%E4%B8%BAF%2C%E7%9B%B4%E7%BA%BFl%E6%96%B9%E7%A8%8B%E4%B8%BAx%3Da2%2Fc%2C%E6%B1%82%E8%AF%81%E6%A4%AD%E5%9C%86%E4%B8%8A%E4%BB%BB%E6%84%8F%E7%82%B9P%E5%88%B0F%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%8E%E5%88%B0l%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B9%8B%E6%AF%94%E4%B8%BAc%2Fa)
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椭圆x^2/a^2+y^2/b^2=1,(a>b>0); 右焦点为F,直线l方程为x=a2/c,求证椭圆上任意点P到F的距离与到l的距离之比为c/a
椭圆x^2/a^2+y^2/b^2=1,(a>b>0); 右焦点为F,直线l方程为x=a2/c,求证椭圆上任意点P到F的距离与到l的距离之比为c/a
椭圆x^2/a^2+y^2/b^2=1,(a>b>0); 右焦点为F,直线l方程为x=a2/c,求证椭圆上任意点P到F的距离与到l的距离之比为c/a
d1=√[(x-c)^2+y^2],d2=a^2/c-x,a^2=b^2+c^2
x^2/a^2+y^2/b^2=1 ====>y^2=b^2-(b^2/a^2)*x^2
则d1/d2={√[(x-c)^2+y^2]}/(a^2/c-x)
={√[x^2-2cx+c^2+a^2-c^2-(1-c^2/a^2))*x^2]}/(a^2/c-x)
={√[-2c^2x+ca^2+(c^2/a^2)*cx^2]}/(a^2-cx)
=(c/a)*{√[c^2x^2-2ca^2x+a^4]}/(a^2-cx)
=(c/a)*{√[(cx-a^2)^2]}/(a^2-cx)
=(c/a)*{1}=c/a
其实x=a^2/c就是此椭圆的右准线,椭圆第一定律就是这样的,第二定律是:某点到两不同定点的距离之和为定值.