问题
填空题
若直线mx+y+n-1=0(mn>0)经过椭圆
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答案
∵直线mx+y+n-1=0(mn>0)经过椭圆
+x2 4
=1的右焦点F(1,0),y2 3
∴m+n=1,
∵mn>0,
∴m>0,n>0,
∴
+1 m
=(m+n)(1 n
+1 m
)1 n
=2+
+n m m n
≥2+2
=4.
•n m m n
∴则
+1 m
的最小值为4.1 n
故答案为:4.
若直线mx+y+n-1=0(mn>0)经过椭圆
|
∵直线mx+y+n-1=0(mn>0)经过椭圆
+x2 4
=1的右焦点F(1,0),y2 3
∴m+n=1,
∵mn>0,
∴m>0,n>0,
∴
+1 m
=(m+n)(1 n
+1 m
)1 n
=2+
+n m m n
≥2+2
=4.
•n m m n
∴则
+1 m
的最小值为4.1 n
故答案为:4.