问题 问答题

过点C(0,1)的椭圆的离心率为椭圆与x轴交于两点A(a,0)、B(-a,0),过点C的直线l与椭圆交于另一点D,并与x轴交于点P,直线AC与直线BD交于点Q。

当点P异于A、B两点时,求证:为定值。

答案

参考答案:

当直线l与x轴垂直时与题意不符。

设直线l的方程为

,代入椭圆方程得(4k2+1)x2+8kx=0。

解得x1=0,

,代入直线l的方程得y1=1,

所以D点的坐标为

又直线AC的方程为

,又直线BD的方程为

联立得

因此

问答题 简答题

飞乐公司为家电生产企业,随着国家家电下乡和以旧换新政策的持续实施,飞乐公司产品销量连续增长,至2013年年末太阳能热水器销量已达到生产线最大产能,遂决定扩大生产能力、租入一条新的太阳能热水器生产线。2013年年末,飞乐公司面临两种方案可供选择。方案一:与乙租赁公司(以下简称"乙公司")签订协议租入生产线。租赁期为2013年12月31日至2017年12月31日,2014年至2017年每年年末支付租金600万元。租赁期满时,A生产设备的估计余值为300万元,均由飞乐公司自行担保。租赁合同年利率为6%,飞乐公司无法获知乙公司的租赁内含利率。2013年12月31日,该生产线在乙公司的账面价值为2500万元,公允价值也为2500万元,已使用3年,预计尚可使用5年。2017年12月31日,飞乐公司将A生产设备归还给乙公司。方案二:与丙公司签订协议租入生产线。丙公司原为家电生产企业,近年主业转为生产电脑及相关部件,导致生产线闲置。租赁期为2013年12月31日至2015年12月31日,2013年至2015年,每年年末支付租金500万元。丙公司该生产线账面价值为2300万元,公允价值为2500万元,已经使用3年,预计尚可使用5年。2015年12月31日租赁期满时归还资产。假设两条生产线型号、生产能力及新旧程度完全相同。2013年12月31日,生产线运抵飞乐公司当日即可投入使用;生产线生产的热水器于生产当年全部对外出售。飞乐公司固定资产均采用年限平均法计提折旧。另外,飞乐公司正在筹备上市,为满足相关法规规定的连续三年盈利要求(2014年为第三年),公司暂缓考虑长期指标,下年经营首要目标是当年盈利最大化。[(P/A,6%,4)=3.4651;(P/F,6%,4)=0.7921;(P/A,2%,4)=3.8077;(P/F,2%,4)=0.9238]

要求:(1)以飞乐公司2014年经营目标为基础,分别对两个方案进行分析,说明飞乐公司应作出的选择。(2)如果飞乐公司选择方案一,编制飞乐公司2017年年末租金支付以及其他与租赁事项有关的会计分录;如果飞乐公司选择方案二,编制丙公司2015年与租赁事项相关的会计分录。

(3)如果飞乐公司选择方案一,计算乙公司的租赁内含利率并编制其在2014年的有关会计分录(结果保留两位小数,金额单位用"万元"表示)。

阅读理解

C

If you gaze(凝视)through a telescope at a distant galaxy(星系), it may glow brightly with the light of hundreds of millions of stars. Despite(尽管,不顾) all that light, most scientists think that at the center of a big galaxy lies something very dark: a black hole. A black hole is a region of space with gravity so strong that nothing can escape, not even light.

Astronomers recently announced they had observed a faraway galaxy that may have at its center two black holes, very close together. Based on their observations, the stargazers suspect one of the black holes has more mass than the other. The more mass something has, the stronger its gravitational force, so a larger black hole has a stronger gravitational attraction. The smaller black hole orbits(作轨道运行) the larger black hole, just as the earth orbits the sun.

The biggest galaxies in the universe form when two smaller galaxies collide(碰撞). If  two galaxies merge(合并), then all of their stars start orbiting a common center. The black holes at the galaxies’ centers should come together, too. Galaxies are colliding all the time, so we should be able to find lots of black hole pairs. But that’s easier said than done—astronomers rarely find these in deep space.

To find a black hole is complicated. A black hole doesn’t produce any light, so how can you find one in space? Astronomers think when something (like dust) falls into a giant black hole, a jet of radiation, a form of energy, may stream away. If this radiation is strong enough, it forms a quasar(类星体).

The Arizona astronomers looked at more than 17,000 quasars and finally found a galaxy that may have a double black hole at its heart. Though the finding of their research is still unconfirmed, and they may be mistaken, the truth will be revealed in the future.

63. Which of the following is TRUE about black holes?

A. A black hole is a region in galaxies with nothing in it, even a bunch of light.

B. Black holes are used by astronomers to study how quasars come into being.

C. When different galaxies meet in space, the black holes become bigger and bigger

D. Some scientists think there’s one black hole in a galaxy, but others think there’re two.

64. From the second paragraph we can infer that ________.

A. a larger black hole pushes a smaller black hole away

B. a larger black hole pulls a smaller black hole toward it

C. the places of black holes are fixed, so we can see them clearly

D. a smaller black hole moves around a larger one because of radiation

65. According to the passage, astronomers think that there should be many black hole pairs because____________.

A. a black hole can produce light

B. black holes can attract one another

C. different black hole pairs come into being with the meeting of galaxies.

D. a big black hole can usually be divided into two small black holes