如果点p(-1/2,1)是直线被椭圆(y^2)/9+x^2=1截得的线段的中点,求直线方程.
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![如果点p(-1/2,1)是直线被椭圆(y^2)/9+x^2=1截得的线段的中点,求直线方程.](/uploads/image/z/14462343-63-3.jpg?t=%E5%A6%82%E6%9E%9C%E7%82%B9p%EF%BC%88-1%2F2%2C1%EF%BC%89%E6%98%AF%E7%9B%B4%E7%BA%BF%E8%A2%AB%E6%A4%AD%E5%9C%86%28y%5E2%29%2F9%2Bx%5E2%3D1%E6%88%AA%E5%BE%97%E7%9A%84%E7%BA%BF%E6%AE%B5%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E6%B1%82%E7%9B%B4%E7%BA%BF%E6%96%B9%E7%A8%8B.)
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如果点p(-1/2,1)是直线被椭圆(y^2)/9+x^2=1截得的线段的中点,求直线方程.
如果点p(-1/2,1)是直线被椭圆(y^2)/9+x^2=1截得的线段的中点,求直线方程.
如果点p(-1/2,1)是直线被椭圆(y^2)/9+x^2=1截得的线段的中点,求直线方程.
设直线方程:y=k(x+1/2)+1
则:[k(x+1/2)+1]^2+9x^2=9
(9+k^2)x^2+k(k+2)x+(k/2+1)^2-9=0
x1+x2=-k(k+2)/(9+k^2)
p(-1/2,1)是线段的中点
(x1+x2)/2=-1/2
k(k+2)/(9+k^2)=1
k=9/2
直线方程:y=9/2*(x+1/2)+1
即:18x-4y+13=0