左焦点:(-4,0)
故可以设L的方程为:y=k(x+4)
代入原来的椭圆方程:9x^2+25y^2=225
9x^2+25k^2(x+4)^2=225
(9+25k^2)x^2+200k^2x+400k^2-225=0①
设两交点为(x1,y1)(x2,y2)
则x1,x2为①的两根
AB=√[(y2-y1)^2+(x2-x1)^2]
=√[(k(x1+4)-k(x2+4))^2+(x2-x1)^2]
=√(1+k^2)|x1-x2|=30/7
由伟达定理:x1+x2=-200k^2/(9+25k^2)
x1*x2=(400k^2-225)/(9+25k^2)
(x1-x2)^2=(x1+x2)^2-4x1x2
=[200k^2/(9+25k^2)]^2-4[(400k^2-225)/(9+25k^2)]
(1+k^2)*[200k^2/(9+25k^2)]^2-4[(400k^2-225)/(9+25k^2)]=900/49
解得:k=√3,-√3
故y=√3k+4√3
或y=-√3k-4√3
计算有些难度,解方程的方法是设元法