如果橢圓x^2/36+y^2/9=1的弦被點（4,2)平分，則弦所在的直線方程是什么？

熱心網友

設弦所在的直線方程為y=kx+b ...(1),其與橢圓交于A(x1,y1),B(x2,y2)則, (x1+x2)/2 = 4, (y1+y2)/2 = 2即: x1+x2 = 8, y1+y2 = 4將(1)代入橢圓方程,化簡,得:(9+36*k^2)*x^2 +72kbx +(36*b^2 -324) = 0== -72kb/(9+36*k^2) = x1+x2 = 8y1+y2 = 4 = k*(x1+x2) +2b解得: k = -1/2, b = 4因此, 設弦所在的直線方程為 y = -x/2 +4, 即: x +2y = 8