p(x,y)是椭圆0.5(x^2)+(y^2)=1上的点,M(m,0)是定点,若pm最小值为(√5/3),则m=?若f(c,0)是双曲线(x^2)/(a^2)+(y^2)/(b^2)=1的右焦点,p在双曲线左支上,线段pf与圆(x-(c/3))^2+y^2=(b^2)/9相切于q.且向量pq=2向
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![p(x,y)是椭圆0.5(x^2)+(y^2)=1上的点,M(m,0)是定点,若pm最小值为(√5/3),则m=?若f(c,0)是双曲线(x^2)/(a^2)+(y^2)/(b^2)=1的右焦点,p在双曲线左支上,线段pf与圆(x-(c/3))^2+y^2=(b^2)/9相切于q.且向量pq=2向](/uploads/image/z/5911337-65-7.jpg?t=p%28x%2Cy%29%E6%98%AF%E6%A4%AD%E5%9C%860.5%28x%5E2%29%EF%BC%8B%28y%5E2%29%EF%BC%9D1%E4%B8%8A%E7%9A%84%E7%82%B9%2CM%28m%2C0%29%E6%98%AF%E5%AE%9A%E7%82%B9%2C%E8%8B%A5pm%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%28%E2%88%9A5%EF%BC%8F3%29%2C%E5%88%99m%EF%BC%9D%3F%E8%8B%A5f%28c%2C0%29%E6%98%AF%E5%8F%8C%E6%9B%B2%E7%BA%BF%28x%5E2%29%2F%28a%5E2%29%2B%28y%5E2%29%2F%28b%5E2%29%3D1%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9%2Cp%E5%9C%A8%E5%8F%8C%E6%9B%B2%E7%BA%BF%E5%B7%A6%E6%94%AF%E4%B8%8A%2C%E7%BA%BF%E6%AE%B5pf%E4%B8%8E%E5%9C%86%EF%BC%88x-%28c%EF%BC%8F3%29%EF%BC%89%5E2%2By%5E2%3D%28b%5E2%29%2F9%E7%9B%B8%E5%88%87%E4%BA%8Eq.%E4%B8%94%E5%90%91%E9%87%8Fpq%3D2%E5%90%91)
p(x,y)是椭圆0.5(x^2)+(y^2)=1上的点,M(m,0)是定点,若pm最小值为(√5/3),则m=?若f(c,0)是双曲线(x^2)/(a^2)+(y^2)/(b^2)=1的右焦点,p在双曲线左支上,线段pf与圆(x-(c/3))^2+y^2=(b^2)/9相切于q.且向量pq=2向
p(x,y)是椭圆0.5(x^2)+(y^2)=1上的点,M(m,0)是定点,若pm最小值为(√5/3),则m=?若f(c,0)是双曲线(x^2)/(a^2)+(y^2)/(b^2)=1的右焦点,p在双曲线左支上,线段pf与圆(x-(c/3))^2+y^2=(b^2)/9相切于q.且向量pq=2向量qf,求双曲线离心率.希望有过程.
p(x,y)是椭圆0.5(x^2)+(y^2)=1上的点,M(m,0)是定点,若pm最小值为(√5/3),则m=?若f(c,0)是双曲线(x^2)/(a^2)+(y^2)/(b^2)=1的右焦点,p在双曲线左支上,线段pf与圆(x-(c/3))^2+y^2=(b^2)/9相切于q.且向量pq=2向
据题意 1,M在椭圆内 以(m,0)为圆心 √5/3 为半径的圆与椭圆正好相切
联立0.5(x^2)+(y^2)=1
(x-m )^+y^=5/9 得 x^-4mx+2m^+8/9=0 (a) (a)的判别式为0 解得 m^=4/9 m=+- 2/3
2,M在椭圆外 易知 M距离长轴√5/3 m= +- (√2+√5/3)
第二题马上就看
设圆的圆心为t ft=c-1/3c=2/3 c qf^=ft^-qt^=4/9 c^-b^ =a^+1/3 c^ 而向量pq=2向量qf,故pf长为根号下(3c^+a^) 设 q的纵坐标/qf= qt/tf 得 q纵坐标 b/6c * 根号下(3c^+a^)
进一步 求出 p的坐标(-c^-a^)/2c ,根号下(3c^+a^)*b/2c) 代入双曲线方程
得a^/c^+ c^/a^ =5 令c/a =x x^+1/x^=5 推出偏心率 根号下 (5+根号21)/2