试题与答案

已知x29+y24=1，则t=yx+6的取值范围为______．

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题型：填空题

题目：

已知
x2
9
+
y2
4
=1，则t=
y
x+6
的取值范围为______．

答案：

t=

y
x+6
可以斜率，t=
y
x+6
的取值范围为过定点

A（-6，0）与椭圆相切的两直线斜率之间．

设过定点A（-6，0）的直线方程为y=k（x+6），代入椭圆方程，得，（

1
9
+
k2
4
）x2+3k2x+9k2-1=0

∵y=k（x+6）与椭圆相切，∴△=0．即9k4-4（

1
9
+
k2
4
）（9k2-1）=0

解得，k=±

2
3
9
．

当过定点A（-6，0）的直线与椭圆有交点时，可看出斜率在-

2
3
9
到
2
3
9
之间．

故答案为[-

2
3
9
，
2
3
9
]

考点：直线与椭圆方程的应用圆锥曲线综合
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编制2012年12月甲公司上述(1)至(10)项经济业务相关的会计分录。
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