问题 填空题
如果椭圆
x2
36
+
y2
9
=1
上的弦被点(1,-2)平分,那么这条弦所在的直线方程是 ______.
答案

设弦AB的两个端点A(x1,y1),B(x2,y2),因为(1,-2)为AB的中点得:

x1+x2
2
=1,
y1+y2
2
=-2.③

代入椭圆方程得:

x12
36
+
y12
9
=1 ①
x22
36
+
y22
9
=1 ②
①-②得:
x12-x22
36
+
y12-y22
9
=0,

化简并将③代入得:

y1-y2
x1-x2
=
1
8
即斜率k=
1
8

所以这条弦所在的直线方程为y+2=

1
8
(x-1)化简得:x-8y-17=0

故答案为x-8y-17=0

单项选择题
问答题

Traditionally, the woman has held a low position in marriage partnerships. While her husband went his way, she had to wash, stitch and sew. Today the move is to liberate the woman, which may in the end strengthen the marriage union. Perhaps the greatest obstacle to friendship in marriage is the amount a couple usually sees of each other. Friendship in its usual sense is not tested by the strain of daily, year-long cohabitation. (46) Couples need to take up separate interests (and friendship) as well as mutually shared ones, if they are not to get used to the more attractive elements of each other’s personalities.
(47) Married couples are likely to exert themselves for guests--being amusing, discussing with passion and point--and then to fall into dull exhausted silence when the guests have gone. As in all friendship, a husband and wife must try to interest each other, and to spend sufficient time sharing absorbing activities to give-them continuing common interests, (48) But at the same time they must spend enough time on separate interests with separate people to preserve and develop their separate personalities and keep their relationship fresh.
(49) For too many highly intelligent working women, home represents chore obligations, because the husband only tolerates her work and does not participate in household chores. For too many highly intelligent working men, home represents dullness and complaints--from an over-dependent wife who will not gather courage to make their own life.
In such an atmosphere, the partners grow further and further apart, both love and liking disappearing. (50) For too many couples with children, the children are allowed to command all time and attention, allowing the couple no time to develop liking and friendship, as well as love, allotting exclusive parental roles.