Who was the author of Annie?

以下是一个关于圆锥曲线中点弦方程应用的教案示例： **一、教学目标** 1. 知识与技能目标 - 学生能够熟练运用点差法求出圆锥曲线中点弦所在直线方程。 - 学会运用中点弦方程解决一些与圆锥曲线相关的几何问题，如求斜率、弦长、轨迹方程等。 2. 过程与方法目标 - 通过对中点弦方程的推导及应用过程，培养学生逻辑推理、运算求解等数学能力。 - 引导学生体会数学中的“设而不求”思想，提高解题效率。 3. 情感态度与价值观目标 - 激发学生对圆锥曲线这一知识点的学习兴趣，培养其勇于探索的精神。 **二、教学重难点** 1. **重点** - 中点弦方程的推导过程及用点差法求解中点弦方程的步骤。 - 运用中点弦方程解决各类圆锥曲线相关问题。 2. **难点** - 根据不同圆锥曲线的性质及已知条件，灵活运用中点弦方程。 - 理解在运用中点弦方程解题时，可能存在的限制条件及需要检验的情况。 **三、教学方法** 讲授法、讨论法、练习法相结合。 **四、教学过程** 1. 知识回顾（5分钟） - 回顾圆锥曲线（椭圆、双曲线、抛物线）的标准方程及其基本性质。 - 提问学生关于中点坐标公式的内容，为后续点差法的推导做铺垫。 2. 中点弦方程的推导（10分钟） - 以椭圆为例，设椭圆方程为\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1\)（\(a>b>0\)），设弦的两个端点为\(A(x_{1},y_{1})\)，\(B(x_{2},y_{2})\)，中点为\(M(x_{0},y_{0})\)。 - 将\(A\)、\(B\)两点坐标代入椭圆方程，然后两式相减，经过化简得出中点弦的斜率\(k =-\frac{b^{2}x_{0}}{a^{2}y_{0}}\)，进而得到中点弦方程\(y - y_{0}=-\frac{b^{2}x_{0}}{a^{2}y_{0}}(x - x_{0})\)。 - 让学生类比推导双曲线和抛物线的中点弦方程。 3. 中点弦方程的应用讲解（20分钟） - **题型一：求斜率** - 例1：已知椭圆\(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)的弦\(AB\)中点为\((1,1)\)，求弦\(AB\)的斜率。 - 解：根据椭圆中点弦斜率公式\(k =-\frac{b^{2}x_{0}}{a^{2}y_{0}}\)，其中\(a = 3\)，\(b = 2\)，\(x_{0}=1\)，\(y_{0}=1\)，可得\(k =-\frac{4\times1}{9\times1}=-\frac{4}{9}\)。 - **题型二：求弦长** - 例2：在双曲线\(x^{2}-\frac{y^{2}}{2}=1\)中，已知弦\(AB\)中点为\((2,1)\)，先求出弦\(AB\)所在直线方程，再求弦长\(AB\)。 - 解：先求出中点弦斜率\(k = 2\times\frac{2}{1}= 4\)，则直线方程为\(y - 1 = 4(x - 2)\)，即\(y = 4x - 7\)。联立双曲线方程与直线方程\(\begin{cases}x^{2}-\frac{y^{2}}{2}=1\\y = 4x - 7\end{cases}\)，消去\(y\)得到关于\(x\)的一元二次方程，利用弦长公式\(l=\sqrt{1 + k^{2}}\cdot\sqrt{(x_{1}+x_{2})^{2}-4x_{1}x_{2}}\)求出弦长。 - **题型三：求轨迹方程** - 例3：设椭圆\(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\)上有一动弦\(AB\)，且弦\(AB\)的中点\(M\)在直线\(y = x\)上，求中点\(M\)的轨迹方程。 - 解：设\(M(x,y)\)，\(A(x_{1},y_{1})\)，\(B(x_{2},y_{2})\)，根据中点弦方程及\(M\)在直线\(y = x\)上的条件，得到\(y_{1}+y_{2}=2y\)，\(x_{1}+x_{2}=2x\)，再将\(A\)、\(B\)代入椭圆方程相减，结合中点坐标与椭圆方程的关系求出轨迹方程。 4. 课堂练习（10分钟） - 布置几道关于圆锥曲线中点弦方程应用的练习题，如求抛物线\(y^{2}=2px\)（\(p>0\)）中点弦斜率、弦长等问题，让学生独立完成。 5. 课堂小结（5分钟） - 总结中点弦方程的推导方法（点差法）及其在不同题型中的应用。 - 强调在使用中点弦方程解题时，需要注意的事项，如双曲线和抛物线解题后的检验等。 **五、教学反思** 1. 成功之处 - 在教学过程中，通过多种题型的讲解，使学生较好地掌握了圆锥曲线中点弦方程的应用。 - 在知识回顾环节，能够有效地引导学生回忆相关知识点，为新知识的学习打下了良好的基础。 - 练习环节有助于及时巩固学生所学知识，通过学生的练习反馈，可以看出大部分学生能够运用中点弦方程解决简单的圆锥曲线问题。 2. 不足之处 - 在推导中点弦方程时，部分学生对“设而不求”的思想理解不够深入，导致推导过程中出现困惑，今后需要增加更多的引导和解释。 - 在讲解应用题型时，个别例题的难度可能偏高，对于一些基础较弱的学生来说理解起来有一定困难，下次教学应更加注重分层教学，根据学生的实际情况调整例题的难度。 - 课堂时间把控不够精准，导致最后的课堂小结略显仓促，下次应更加合理地安排每个教学环节的时间。 <a href="/?from=ask_words" style="color:red" target="_blank">点击前往免费阅读更多精彩小说</a>

Here are some names suitable for girls in fantasy novels: 1. ** Light Smoke **: The original meaning was light smoke, filled with a fantastical haziness. 2. ** Bi Fan **: The word 'Bi' represents a green jade stone, giving people a fresh and precious feeling. 3. ** Shadow Ink **: It has the artistic conception of " half a green lamp and a piece of paper, the lonely lamp only reflects the ink of this life ", full of poetry and mystery. 4. ** Ruo Nan **: The word 'Ruo' means 'seems' or 'if'. The word' Nan 'refers to Nanmu, which means that people are as precious as Nanmu. In fantasy stories, it can also mean that they have something to rely on. 5. ** Hidden as **: From "Auspicious in inaction, hidden as the southwest corner." He had a mysterious and low-key temperament. 6. ** Mu Xian **: The word 'Mu' represents attachment, yearning, and so on. The word 'Xian' represents the girl's petite and delicate beauty, creating a beautiful and magical feeling. 7. ** Zi Ni **: The purple character represented elegance, nobility, charm, and confidence. The purple character pointed to the white rainbow and was filled with a magical and gorgeous feeling. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

I recommend a few super interesting ancient romance novels. Feifei Xiao's << The Elder Princess of Time Travel: Lucky >> was a story of the modern day's White Bone Demon Mu Shi transmigrating into a silly elder princess. She had a spiritual pet, a space, and a handsome guy. Her life was extremely carefree. Wang Cai was a cat who wrote " After I Transmigrated, I Was Dragged Down by a Bamboo Horse and Became an Empress." Gu Jingyao was transmigrated into a fool after a car accident and was " married " into the Prince's mansion by her unscrupulous parents. In the end, it was a mistake for a fool to marry a fool. Neither of them were stupid. Ling Bing 'er's " Little Husband and Wife of the Ming Dynasty " was reborn as the foolish young lady of the Minister's Mansion. Although she suffered many unfairness, she worked together with her husband to foil the plot and even gained happiness. In Sesame Ball's " The Emperor's Wife," the female protagonist had mistakenly transmigrated and forgotten her modern identity. After entering the palace as a concubine, she was in endless trouble. In the cute prince's " Husband from Another World, Turn Over ", Leng Qingyou could only be a " vixen " when she transmigrated. Her husbands were all animals, but there were many handsome men and many benefits. The male lead, the wizard beast Green Lotus, could not speak and could only be a vegetarian. He was quite handsome. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

" C-Class Half-Blood Forced to Slay a Dragon " was a very unique Dragon Doujinshi novel. The main character, Luo Yin, was a C-level student at Kassel College. He was as reliable as Doraemon. His bloodline level was low, but he unexpectedly had a dragon language analysis system. He relied on alchemy and his liver to survive in the academy and slay dragons. The novel had its advantages and disadvantages. The advantages were that it had a good point of entry, was creative, and had a good operation of bringing Dragon Three forward. The disadvantages were that the writing style and narrative angle needed to be improved. The battle description was too long, and the author did not have a deep understanding of alchemy. However, it completed the world view, and it was still a masterpiece of food and grass. " Here I Come, Reborn " was a modern romance novel. It was a story about gathering money and having a happy family. " The Twins in the Storm " was a modern romance novel. The older brother brought the younger brother back to life and had fun. There was a special bond between the twins. " When I Wake Up, I Become the Female Deskmate's Father " was a big idea. The male lead became the female deskmate's father. It was an entertainment novel with a double coat. It was creative in the early stages but weak in the later stages. It even ended badly. " 1993 " was an urban nanny novel. The male protagonist woke up with two children. The mother of the children passed away during childbirth. He began his journey as a nanny, but unfortunately, he was a eunuch. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

Here were some celebrities who had the air of an overbearing CEO: - ** Male Celebrity **: - [Ming Dao: His appearance, height, and temperament are very much in line with the image of an overbearing president. His every move shows the innate aristocratic aura of an overbearing president. The characters he played in dramas such as " The Prince Becomes a Frog " are deeply rooted in people's hearts. Even if he doesn't play such a role, people can still feel the temperament of an overbearing president.] - [Jin Dong]: The boss he played looked cold, but he was deeply affectionate and loyal. He behaved like a gentleman, spoke well, and was mature and steady. - Wang Hedi: Dressed in a suit and leather shoes, wearing gold-rimmed glasses, his looks and temperament are outstanding, giving people the feeling of a handsome and domineering CEO. - [Wang Yaoqing: Boss has a strong aura. He has a domineering aura. He is like a king who has descended. No one can ignore him.] - [Dennis Wu]: Deep eyes, well-defined facial features, tall figure, handsome and cool when acting as a domineering president. - [William Li: Tall and slender, his actions and mannerisms reveal the unrestrained and elegant side of a domineering president.] - [Zhong Hanliang: His boss has a strong personal charm. He is domineering and cold. He has a strong aura.] - ** Zhang Han **: Tall and tall, every move carried extraordinary confidence, and his image as a CEO left a deep impression on people. - ** Yang Yang **: He has a face like a prince. He is handsome and has an aristocratic temperament. He shows the gentlemanly and gentle side of a CEO. - Kaiwei Liu: The president he played was a combination of elegance and confidence. His appearance exuded the charm of a mature man. - [Zhu Yawen: His image of a tyrant in a suit shows the temperament of a yuppie. He is handsome and very manly.] - ** Female Celebrity **: Zhao Liying wore a simple and elegant suit at a public event. With exquisite makeup and accessories, she showed a noble and cold temperament. She walked on the stage calmly and confidently. Her powerful aura was like the arrival of a domineering CEO. Moreover, she was determined and determined. This inner strength also reflected the domineering CEO style. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

From a scientific point of view, the possibility of catching a real dinosaur in modern society was extremely low. According to current scientific research, dinosaurs were basically extinct during the Victorian-Paleogene extinction event 65 million years ago. Birds were now considered descendants of dinosaurs, but they were very different from dinosaurs in the traditional sense. If a man really claimed to have caught a real dinosaur, there might be the following situations: one was a misunderstanding of a certain fossil or model of a certain ancient creature; the second was that he encountered a very rare, undiscovered large reptile creature, but it was almost impossible to be a real dinosaur; the third was deliberately creating a gimmick to make a false claim. The novel " White Dragon of the Dragon Clan " is equally exciting. Everyone is welcome to click and read it!

The original singer of 'Mother' was Geng Weihua. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

Running a race against life meant making full use of every minute and second in a limited life, actively striving, striving, and working hard to accomplish more meaningful things, not letting life go to waste. Life had a time limit, just like a candle that would eventually burn out. Time did not stop and passed quickly. When one was resting, time would also pass quietly. Therefore, one had to cherish time, display its due value, continue to work hard, and contribute to society. For example, in the medical scene, medical staff raced against time to save the patient's life. This was also a manifestation of the race against life. They were fighting for time with the god of death and fighting for a chance to save lives within a limited time.

He recommended a few good novels. " Reborn Sweet as Honey " was a modern romance novel written by Zhao Nuannuan. The female lead had been reborn to take revenge. The male and female lead settings were very interesting. " The Hunting Wife Plan ". It was created by a deer named Wen Wen. It was a modern romance genre. The male protagonist had liked the female protagonist since the first year of high school. It was a story about a big bad wolf chasing a little white rabbit. It was very warm and interesting. "Flowers Blossoms and Spring Warmth" was an ancient romantic masterpiece. The female protagonist was reborn in ancient times and depended on the nanny for survival. The story was warm. Although the plot was a little old-fashioned, the writing was good. Listening to Falling Flowers 'writing style was exquisite, light, and the character description was very good. I Build an Immortal Court in the Human World, a Xianxia novel written by Fragrant Sweat and Thin Shirt. The male protagonist, Xu Boqing, went to a strange world and had a game character skill. He entered the palace as a fake eunuch. There were many female protagonists and few emotional scenes. The plot was exciting. Mortal: Starting from Yellow Maple Valley as a Disaster Cultivator. It was a Xianxia novel by Zhou Zhuang, who did not dream of butterflies. The male protagonist, Li Yang, was decisive in killing, while the female protagonists had different personalities. It was a story about mortals pursuing the immortal path. Each of these novels had its own characteristics and were worth reading. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>

There were several movies named Eyewitness. The following are the introductions of the different versions of the movie: ** I. Version released in the mainland of China on November 20, 2012 ** Directed by Gao Zehao, it was about a few middle-aged men who were entangled in a fight because of a traffic accident. In the end, they realized that their seemingly destined fate was actually manipulated by others. ** 2. Version released in Korea on August 15, 2018 (also known as "Fatal Witnesses"(TV),"The Witness')** Directed by Cao Guizhang, the total duration was 111 minutes. The story began with Shang Xun, who witnessed the murder in the garden downstairs on his balcony. After he was discovered by the murderer, he launched a fatal pursuit. The film showed the real problems that modern society might face from a close to life perspective, and revealed the identity of the murderer at the beginning, causing the audience to think about what they would do if they were Shang Xun. The film was set in a large apartment complex, focusing on the reactions and psychological activities of different people in the face of murder. It won the Korean box office in its first week of release, accumulating 21.16 billion won as of September 2,2018. In addition, there was another movie that involved a "witness" in the plot: It was a sci-fi mystery film called "Soul Catching." The story took place in 2032. The famous tycoon Wang Shicong was killed in his home. His wife, Li Yan, was unconscious and holding a blunt weapon in her hand. Initially, it was thought that the murderer was Wang Shicong's son, Wang Tianyou, who had run away from home. However, Liang Wenchao, the prosecutor in charge of the case, found that there was something else behind it. Li Yan was also suspected, and the case was full of twists and turns. Although this was not a movie called Eyewitness, it had a plot mode that was similar to eyewitnesses providing clues and reversing the truth. "The Silent Eyewitness" novel is equally exciting. Everyone is welcome to click and read it!