After taking the advice, I became a top student.
Chapter 24 Effort is also a kind of talent
After scanning through the newly received suggestions, Chen Mo did not hesitate and immediately got up and walked towards Lin Weiwei.
"You just said you wanted me to explain a problem to you, what don't you understand?"
Lin Weiwei looked up at Chen Mo, somewhat bewildered.
Playing hard to get?
Chen Mo's actions undoubtedly attracted the attention of the whole class. He took the initiative to explain the problem to the class beauty, and his intentions couldn't be clearer.
Everyone couldn't help but look at Shen Qingyi beside her, and a flurry of gossips erupted in their hearts.
However, Shen Qingyi continued to do her own thing, seemingly unconcerned about what was happening here.
Zhou Hao sneered, his gaze towards Chen Mo filled with mockery.
The last big question was indeed a bit difficult, but it was just that the calculations were quite extensive and he didn't have enough time, so there was no need to explain it.
He had initially felt a bit threatened because of Chen Mo's extraordinary performance in mathematics, but now it seems that the kid has become complacent after suddenly becoming rich, so there's no need to worry about him anymore.
"Could you explain the last question to me?"
After hesitating for a moment, Lin Weiwei took out a math test paper and said to Chen Mo.
"no problem."
Chen Mo took the pen and draft paper, and explained as he wrote.
First, let's look at the question.
The focus of the parabola C: y^2=4x is F. The line l passing through F intersects C at points A and B. If the perpendicular bisector l1 of AB intersects C at points M and N, and P lies on the line x=1/2, and |PA|*|PB|=|PM|*|PN|, find the equation of l.
"Seeing |PA|*|PB|=|PM|*|PN|,
The first thing that comes to mind is the power of a circle theorem. Therefore, the four points are concyclic. Since these four points lie on the parabola, the sum of the slopes k1 and k2 of line AB is 0. Also, AB is perpendicular to MN, so k1k2 = -1. Using a quadratic equation in two variables, we can find that the slope of AB is either 1 or -1.
"Given a point F on AB, which is the focus of the hyperbola, F(1, 0). Knowing a point and the slope, we can write the equation using the point-slope form: when k1=1, y=x-1; when k1 equals -1, y=-x+1."
Chen Mo finished explaining the final question in less than a minute.
However, when Lin Weiwei looked at Chen Mo, her large, bright eyes were filled with a clear sense of foolishness.
Not only her, but even Shen Qingyi, who was doing practice problems next to her, looked up at Chen Mo.
She also got a perfect score in math this time, but obviously, she didn't do it this way. She spent a full half hour calculating the problem, while Chen Mo only needed one minute.
Shen Qingyi stared blankly at Chen Mo.
"Didn't you understand?"
Chen Mo frowned slightly.
"I know the power theorem."
Lin Weiwei didn't try to sound knowledgeable; she genuinely didn't understand. "But why is it that if four points are concyclic and all four points lie on a hyperbola, the sum of the slopes of the two lines equal to zero?"
"Isn't that obvious?"
Chen Mo was also confused. When he first heard Lin Weiwei's question, he felt a sense of helplessness, as if others were asking him why 1+1=2.
Sometimes he even thought, forget it, it's better not to earn this benefit.
However, since several minutes had already been wasted, Chen Mo decided to go into more detail.
Ultimately, it was the sunk costs that were at play.
Take the draft paper,
「既然你知道圆幂定理,那幺我们设双曲线方程为 x^2/a^2-y^2/b^2=1,两条直线AB:y=k1x+b1,CD:y=k2x+b2。」
「然后我们构造他们交点的曲线系,(k1x+b1−y)(k2x+b2−y)+λ(x^2/a^2−y^2/b^2−1)=0,这个方程表示所有经过四交点的二次曲线的集合。」
"When these four points are concyclic, there exists a λ such that the entire equation represents a circle. Everyone knows the equation of a circle: (x-a)^2 + (y-b)^2 = r^2. It has no xy terms, and the coefficients of x^2 and y^2 are equal."
"So we expand this equation and find that the coefficient of the xy term is -(k1+k2)−(k1+k2). If we want this equation to represent a circle, we need to eliminate this term, which means we must have k1+k2=0."
As Chen Mo explained, Lin Weiwei's eyes began to brighten.
She never expected that the problem that had troubled her for almost half an hour would be so simple.
She had initially doubted Chen Mo's ability to get a perfect score in math, but after he explained the problem, she was filled with admiration.
On second thought, Chen Mo had only studied diligently for less than a month and was already able to achieve this level, while she herself had studied hard for several years but was still a blockhead.
Sometimes she really envied those talented people, which made her feel ashamed of herself.
Zhou Hao, who was standing to the side, had already lost his focus.
He was sitting diagonally behind Lin Weiwei, so it was hard for him not to hear Chen Mo's explanation.
He could naturally think of the power of a circle theorem. If he didn't know the power of a circle theorem and the fact that the four points are concyclic, he wouldn't have been able to solve this problem. But he didn't think of using a hyperbola and two straight lines to construct a system of curves, and then using the characteristics of the circle equation to obtain an equation for the slope.
If he had thought of that, he wouldn't have missed out on a perfect score because of time constraints.
He should have gotten a perfect score too!
Regret gnawed at Zhou Hao's heart.
"You're amazing! I really admire your talent!"
Lin Weiwei looked up at Chen Mo and exclaimed in sincere admiration.
Chen Mo shook his head, "Hard work is also a talent. Keep it up!"
This is not encouragement, but rather a heartfelt expression of feeling.
He has achieved what he has today entirely through his own hard work!
Just then, a barrage of comments popped up.
[Complete the suggestion: Explain the problem to your classmate and make sure they understand. Reward: +66 Nutrients]
Chen Mo was in a very good mood. He spent less than ten minutes explaining the problem, yet he gained a lot of valuable insights. The cost-effectiveness was quite high.
"If you have any questions in the future, you can ask me anytime."
Chen Mo said to Lin Weiwei with a happy expression, as if explaining problems to Lin Weiwei was such a joyful thing.
The genuine smile on Chen Mo's face made everyone feel his joy.
Everyone subconsciously looked at Shen Qingyi on the other side.
But they found that Shen Qingyi was in a daze.
Is hard work also a kind of talent?
Shen Qingyi recalled Chen Mo appearing in the classroom at five in the morning.
Without letting her mind wander, Shen Qingyi focused her attention back on the exercises in front of her.
Chen Mo returned to his seat and began memorizing English words.
Little did he know that his words would be interpreted differently by others.
Lin Weiwei's cheeks flushed instantly, and she looked at Chen Mo with a bright red face. Although she felt a little embarrassed, she didn't know why, but seeing the big boy in front of her with such a happy smile, she was inexplicably moved and felt warm inside.
Is hard work a kind of talent?
Looking at Chen Mo's retreating figure, his eyes were somewhat vacant.
The other students immediately booed.
Several female classmates looked at Lin Weiwei with envy. When Chen Mo's grades were at the bottom, quite a few girls wrote him love letters. After all, his physical attributes were there, so he was still very competitive.
She has now become a top student in her class, and her attractiveness has skyrocketed. They wish they could replace Lin Weiwei.
However, since this person was Lin Weiwei, they couldn't muster any competitive spirit. They couldn't compete with her academically or in terms of physical abilities. How could they compete?
Moreover, there's also Shen Qingyi.
There was no place for them around Chen Mo anymore.
"Old Chen, you've changed!"
Li Ze shook his head repeatedly, "I still prefer your unruly side."
You'll Also Like
-
I have the best bloodline
Chapter 569 16 minute ago -
The saintess I possessed had a head full of nonsense.
Chapter 255 16 minute ago -
The Byakugan Princess of Konoha
Chapter 499 16 minute ago -
I picked up attributes in Swallowing Star.
Chapter 384 16 minute ago -
One Piece: Buggy the Clown Who Fell From Grace
Chapter 453 16 minute ago -
Super God: Rise of Civilization
Chapter 1062 16 minute ago -
Planting an immortal tree in the wizarding world.
Chapter 258 16 minute ago -
The Peerless Tang Sect: Possessing Huo Yuhao at the Start
Chapter 167 16 minute ago -
Primordial Era: I, Huanglong, have refined all the heavens, and will not join the Chan Sect.
Chapter 282 16 minute ago -
Primordial Era: Exceptional Comprehension, Destroying Buzhou Mountain at the Start
Chapter 394 16 minute ago