The system development of a scholar

Chapter 8

The title of this question is this:
Let the focus of the parabola C: y^2=4x be F, and the straight line L passing through F and having a slope of k (k>0) intersect with C and two points A and B, |AB|=8
(1): Find the equation of L

(2): Find the equation of the circle passing through points A and B and tangent to the directrix of C
Xu You took the draft book and said while writing: "This question is not too difficult. From the meaning of the question, we can get F(1, 0), and the equation of L is y=k(x-1)(k& amp;amp;amp;amp;gt;0)

然后我们把未知的A，B两点设出来，代入到L的方程和C的方程中可以得到：k^2x^2-（2k^2+4）x+k^2=0，所以就能得出x+X=（2k^2+4）/k^2，

|AB|=|AF|+|BF|=（x+1）（X+1）=（4k^2+4）/k^2
Because |AB|=8, we assume that 8=(4k^2+4)/k^2, the solution is that k is equal to plus or minus one, because -1 does not fit the meaning of the question, so it is discarded,

So the equation of L is: y=x-1. "

After speaking smoothly in one breath, Xu You looked up at Wang Ya and asked, "Do you understand?"

Wang Ya looked at him and nodded blankly, "Understood."

"Okay then, let's look at the second question."

Xu You bowed his head and continued to write on the draft paper, "From the first question, we can get that the coordinates of the midpoint of AB are (3, 2), so we can get the equation of the perpendicular bisector of AB: y-2=-(x -3), y=x+5,

Let the coordinates of the center of the desired circle be (x, y),
Substituting into two sets of equations can get two sets of answers: x=3, y=2 or x=11, y=-6,

所以圆的方程就是：（x-3）^2+（y-2）^2=16
或（x-11）^2+（y+6）^2=16。”

Putting down the pen, Xu You raised his head and said, "It's troublesome when solving the problem. I omitted the two basic points and didn't write them out. You should know and understand."

However, what he saw was Wang Yawei's mouth opened slightly, looking at him in bewilderment.

Xu You asked: "Why, I don't understand? How about I explain it again..."

As Xu You picked up the pen, although he thought he understood everything, Wang Ya was a little better than himself, even if he didn't understand, after his simple explanation, he should understand.But since he didn't understand it, it didn't matter if he said it again. It happened that he could think through his thinking again, and maybe he could think of another simpler way of thinking.

"Uh... I get it, I don't need to say it a second time." Waking up from his own shock, Wang Ya saw that Xu You had picked up a pen to write on a new page of draft paper, and quickly took it back with a smile. information book.

There is an embarrassment and politeness in the smile...

In fact, she didn't ask Xu You questions from the bottom of her heart, but just a random thought.

Wang Ya's academic performance is higher than Xu You's overall, especially in English and mathematics. Although there is still some gap compared with the top students in the class, compared with Xu You, it is crushed. The scores are all higher than half of Xu You's score.

But she never expected that Xu You would be able to explain a question to Ye Shen that she thought was extremely difficult and she would be able to explain it to her clearly after reading the question once. !

"Didn't he write indiscriminately?"

Unwilling to believe that Xu You could solve such a difficult problem, Wang Ya suddenly had such an idea in her heart.

"Well, it must be for pretense, scribbling!"

Wang Ya turned around and said with a smile: "Xu You, give me the draft just now. I don't understand something very well. I want to read it again."

In her heart, she wanted to use Xu You's draft to prove that Xu You just told her indiscriminately, but she didn't know it at all!

"Do you want me to explain it to you again? Anyway, I haven't attended class yet." Of course, Xu You didn't know Wang Ya's careful thinking, so he asked enthusiastically.

"No need, no need, I can just read it by myself, so I won't delay your study." Wang Ya quickly waved her hand, and after getting Xu You's draft, she couldn't wait to turn around and bow her head to study.

first question...

correct!

Second question...

correct!

"how so!!"

After carefully checking it twice, except for the few steps that Xu You said was omitted, the other steps of solving the problem are well-founded and well-organized. They are simply standard answers!

uncomfortable...

So sad……

Can't breathe...

"Give you."

After searching twice, even with a nitpicking mentality, Wang Ya still couldn't find anything wrong, so she had to give up and bring back Xu You's draft.

"Meet?" Xu You asked after taking it over.

"……Um."

Taking a deep look at Xu You, and covering her heart with her hands, Wang Ya nodded, and then turned around.

Although she was very unwilling to admit defeat, and let a scumbag do the questions she couldn't do, but the facts were in front of her eyes, and she had to believe it.

Perhaps because of the psychological blow, Wang Ya's attention to Xu You increased significantly, and she always kept peeking at Xu You intentionally or unintentionally during evening self-study.

In fact, her mind was very simple, she just wanted to see if Xu You was studying hard or just pretending.

However, Li Zhen and Liu Shen, who had a panoramic view of Wang Ya's small movements, looked at each other, and then saw the flames of gossip in each other's eyes...

Throughout the evening self-study, Xu You lowered his head to write papers. He didn't even raise his head during the 10-minute break after class, completely immersed in the sea of ​​questions.

"Ah~"

Finally, 5 minutes before the end of get out of class, Xu You finally finished two papers, one math and one physics.

The mathematics paper is relatively simple, and the scope of the test is within a book, and the difficulty is comparable to that of the final exam; the physics paper is Xu You's newly bought review paper, which covers comprehensive knowledge points and is not easy.

After moving his stiff spine, Xu You couldn't wait to turn on the system, wanting to see the progress of his mission.

"Why only 37/200?!"

There are a total of 48 questions on the two papers, but the task progress has only increased by 37. What's going on?

After thinking for a while, Xu You suddenly said, "Could it be because you only got 37 questions right?"

Due to the hard work of reviewing the liver questions in the past two days, he has memorized a lot of knowledge points. Although Xu You feels that it is easier for him to do the questions than before, he is not so conceited if he wants to achieve full marks.

After the evening self-study, I came home and took out a pair of answers. Sure enough, Xu You got a total of 37 questions correct in the two papers!

"It seems that this task is both quality and speed."

Now that he knew which questions were wrong, Xu You simply corrected them, and he went through the correct questions along the lines of the reference answers.

After working until 12:30, Xu You finally understood all the questions on these two papers. Regarding the knowledge points involved, he also sorted out the levels and memorized them in his mind.

After going to bed and falling asleep, Xu You walked into that classroom again in his dream, but tonight it was not Teacher Zhao who taught mathematics, but a female teacher surnamed Zhou who taught Chinese.

Unlike Mr. Zhao, who takes the knowledge points of the first year of high school as the basis to go deeper and review systematically, Mr. Zhou speaks Chinese very simply. He gives Xu You an article for him to analyze, and then asks questions by himself. Let Xu You do a propositional composition in class, and then talk about the problems in his composition after finishing it...

So in the cycle of attending classes during the day, doing self-study questions and doing tasks at night, and dreaming and reviewing at night, the time passed quickly, and it was Thursday in a blink of an eye.

Almost a week had passed, and Xu You's hard work was not only seen by his classmates, but even the teachers of various subjects could clearly feel Xu You's progress in study.

Although the range is not too large, as long as there is an attitude, it is good.

Among them, Mr. Guan, the English substitute teacher, felt the weakest, and could barely detect it...

Therefore, in the eyes of Liu Shen and Li Zhen, Xu You has undergone earth-shaking changes, and unconsciously, the looming aura of a master of learning is lit up on his head.

Liu Shen seemed to feel that he had underestimated the man Xu You. Taking advantage of Ma Jian who was not paying attention, he whispered to Xu You, "Why don't we just let it go?"

The questions on the blackboard happened to Xu Youhui, and the thinking and method of solving the questions were exactly the same as what the teacher said. It’s okay to be distracted, so he asked, “What bet?”

Liu Shen paused, and then reluctantly said: "That is... if you can counterattack and become a top student, I will live broadcast the one that eats Xiang."

After a few days of observation, Liu Shen felt that he was younger...

I can't afford to mess with this man...

"Is there such a thing?"

He spent almost 24 hours a day listening to lectures and brushing up on questions. Except for various knowledge points and formulas in Xu You's mind, he selectively forgot some irrelevant things.

He thought about it for a while, and then he remembered that there was such a thing, and then he smiled and said, "Who said that 'a man is a real man, once you say something, it's hard to follow'?"

Old Liu Shen blushed, and said with a smile: "Brother Xu, you are a man who is about to be called a god, why bother with me, a mortal? Forget it."

"Hehe," Xu You laughed twice, and said, "Forget it, but you have to promise me one thing."

"Okay, what's the matter?" Liu Shen immediately agreed.

Xu You said: "I haven't thought about it yet, I'll let you know when I think about it."

"Uh……"

Liu Shen had an ominous premonition in his heart, and asked anxiously, "It can't be something...perverted?"

Ma Jian started to talk about the next question, Xu You made a mistake, so he ignored Liu Shen and listened carefully.

"Am I... am I young again?"

Looking at Xu You's serious and glowing side face, Liu Shen's heart felt a little creepy...

(End of this chapter)