Question

已知抛物线C:y^2=x和直线L:y=kx+3/4,要使C上存在着关于L对称的两点,求实数的k取值

已知抛物线C:y^2=x和直线L：y=kx+3/4，要使C上存在着关于L对称的两点，求实数的k取值范围.

求大家了给我个完整的答案

Answer 1

这个题可以分为两步：
第一步：
y^2=x和y=kx+3/4联立形成关于x的二元一次方程组，由于直线和抛物线必须相交于两个不同的点，所以由两个不同的解得到判别式大于0，从而得到一个k的取值范围；
第二步：
在抛物线C上取两个点A(y1^2,y1)和B（y2^2,y2）然后根据点到线的公式表示出A点到直线L的距离d1和B点到直线L 的距离d2,由题意知道d1=d2,由这个式子可以得到一个包含关于y1和y2的偶次方和包含k 的式子，然后将这个式子化为用y1和y2表示的k的式子，即：k=(一个包含y1^2n和y2的^2n式子)，然后根据这个式子求出一个k的取值范围；
最后两个k 的取值再求交集，就OK了

Answer 2

先找出与抛物线相交2点的直线，再求出该2点的中垂线即可。
与抛物线相交2点的直线的斜率<1/2
故k<-2

Answer 3

Yangcheng Evening News reporter Yang Hui, Cui Jiefeng correspondent reports: the afternoon of August 30, Panyu District Prosecutor Huang Jiewen Deputy Attorney General and his party in the street with wide bi Luopu child care center director and other refined in a meeting. Huang Jiewen Deputy Attorney General (hereinafter referred to as yellow check), said Tong Tong father stepmothers abuse did not cause serious results,air griffey max 1 black, which is a typical case of private prosecution,air griffey max 1 Fresh water, according to the statutes, by the Tong Tongs mother to the courts, however, children His mother has been temporarily charged Procuratorate said. Yellow check that this incident is concerned, Chinas current law to strengthen protection of children there need to be perfected.
by Tong Tong mother sued
Procuratorate of this discussion,air griffey max 1 red, is a child care center before going wide Bi District Prosecutors Office on the Tong Tong was hungry, abused to make a report of response. For the spread of the Internets Procuratorate is not accepted as the final argument, yellow check explained, "This is their (Internet rumors) of the law and prosecutors responsibilities misunderstanding. Procuratorate held for the protection of children is the same attitude with you." .
event for the legal application of Tong Tong, Huang explained in detail check: Chinas Criminal Law Article 260 provides that "abuse of family members, aggravated, at two years imprisonment, criminal detention or control. Resulting in victims of serious injury or death, at two to seven years imprisonment.s first crime, told the only treatment. "Article 98 of the Criminal Code states: this law to be handled, is the victim to be handled. If the victim due to coercion, intimidation can not tell, the Peoples Procuratorate and the victims close relatives can tell. According to "Criminal Law (sub) and supporting the new release provides a new solution": the so-called handled only upon complaint, the victim is to sue the peoples court, the court was dealing with, do not tell does not deal with. Purpose of this legislation, mainly on account of abuse cases occurred in family members, relatives of the abused who do not want to break the relationship,ken griffey shoes, but do not want to resort to the judiciary for conviction and sentencing of abusers. Therefore, to fully consider the wishes of those who were abused. But according to the regulations, if the abused person by force, intimidation,nike air diamond turf, etc., can not the peoples court, the Peoples Procuratorate may prosecute. Abused by other close relatives can also sue the relevant units and organizations can also intervene to expose the Peoples Procuratorate,griffey sneakers, Peoples Procuratorate verified by the prosecution.
"causing the victim serious injury, death, at two to seven years imprisonment." Refers to the victim caused by the gradual long-term physical abuse or serious injury leading to death, or because the victim unable to bear the long-term abuse The suicide death or serious injury results, the perpetrator is intentionally abuse, and negligence to cause another person serious injury or death results, the abuse and injuries,nike air griffey max 1, the consequences of death between the criminal law have a causal relationship. According to which the abuse victim resulting in serious injury or death cases are the prosecutions case. In such cases, even if the victim does not sue, the public security organs should also be investigation by the prosecution to prosecute.
yellow check that the issue is on the Tong Tong, from the current evidence,air jordan heels, Tong Tong father, stepmothers abuse did not cause Tong Tong serious injury or death results, and thus the case is a typical case of private prosecution, but also Tong Tong was due back to Hong Kong to take care of their mother, so there was no coercion,nike air griffey max fury, intimidation and can not prosecute the case to the court, so this case to the courts by its mother is the most current law practice.
child protection laws need to be improved
Procuratorate had contacted Tong Tongs mother, she clearly explained to the relevant laws and regulations, but temporarily Tong Tongs mother made it clear that prosecution. Therefore,nike air max jr 2011, the police,ken griffey shoes, the prosecution can not be involved in the process of private prosecution. This investigation is not public security organs, the prosecution can not start filing the monitoring process.
heard on the yellow check detailed explanation from the law, the broad center of the refined Bi chairman, director, "a piece of cake," said the center has been caring for the District Prosecutors Offices attitude towards the incident, efforts are understandable,ken griffey shoes 2011, they are not pursuing the incident must have, what kind of results, just want this event to those who intentionally or unintentionally, to deter people who abuse children,griffeys shoes, so that they can not do whatever they want. For Tong Tong has been living in Hong Kong back to its mother and well cared for, care centers are two members that this is a very satisfactory result.
two care center director said that the current law there are loopholes in this regard, yellow check explain each countrys own legal system different from the law itself has a certain lag, the prosecution is the legal applicable authorities, rather than the legislature, the prosecution can only be exercised within the limits prescribed by law their powers. For this special group of enhancing the protection of children, yellow check, feels that our laws there need to be perfected.
"For example, this incident is concerned, Tong Tong is due to hunger leads to malnutrition,ken griffey jr sneakers, then, can develop more specific identification criteria,nike air griffey max fury 2012, clear to what degree of malnutrition which is equivalent to minor injuries, injured grade it? they can relax or prosecution of cases of this particular subject, so wide Bi charity care centers such social organizations in civil society under certain conditions can also sue on behalf of Tong Tong it? "Huang said inspection.