Xu Zongyun was stunned!
After Xu Heng finished speaking and he posted this sentence in the group, everyone fell silent.
Damn...! ! !
They really haven't considered it.
After all, it is the final question of filling in the blanks. It is already very good to be able to do it.
How can there be time to consider the second method!
But Xu Heng saw that everyone was silent.
He said directly, "So, do you understand why I am looking for this test paper?"
Xu Zongyun also understood it immediately.
"Doing the questions is secondary... The main thing is to let me learn to answer questions with different thinking methods?!"
"hiss……!"
For an instant.
Xu Zongyun's opinion of Xu Heng has once again been raised a lot.
It turned out that every time Xu Heng did something, it was purposeful!
And it's very purposeful!
It's just that Xu Zongyun doesn't understand!
"I'm sorry! Brother! It's because I'm ignorant!"
Xu Heng put down his phone, pointed to the question and said, "This question can use the formula of double radius and single intersection line."
说着,许衡在旁边写下:R2=R12+R22-L2/4。
"The formula is like this..."
"If the two planes are perpendicular to each other, and the radii of the circumscribed circles of the respective convex polygons in the two planes are R1 and R2 respectively, and the common chord length of the circumscribed circles of the two planes is L, then the circumscribed circle of the convex polyhedron formed by connecting the vertices of the convex polygons in the two planes The circle radius is the formula I just wrote."
"Remember the formula, if you prove it, I won't repeat it!"
"With this formula, the solution to this problem is easy!"
"Let's look at another question next."
Xu Heng pointed to the last finale question.
Hyperbola C: (x2/a2)-(y2/b2)=1(a0,b0) The left vertex is A, the right focus is F, the moving point B is on C, when BF⊥AF|AF|= |BF|, find the eccentricity of C; if B is in the first quadrant, prove: ∠BFA=2∠BAF.
When Xu Heng started to focus on this question, Xu Zongyun immediately frowned, "Brother! This question...can't have an easier solution?!"
But as soon as he finished speaking, Xu Zongyun regretted it.
Because the person in front of him is Xu Heng!
Even if Xu Zongyun was sure, but in front of Xu Heng, he still murmured in his heart.
After all, Xu Heng would not bring up this question for no reason.
……
PS: It seems that the chapter was sent wrong just now, and now it has been corrected and replaced!Everyone, go back and refresh, and you can watch 260!
Two updates together!Kneel for all support! .
Chapter 264
Xu Heng looked at Xu Zongyun's way of solving the problem:
Let P(m,n), F1(-c,0), F2(c,0)...
……
即有c2=3,即c=根号3,又e=c/a=(根号3)/2,可得a=2,b=根号下(a2-c2)=1,则椭圆的方程为(x2/4)+y2=1。
……
Assuming A(x1, y1), B(x2, y2), M(-2,0) can be obtained according to the meaning of the question. If the slope of the straight line AB does not exist, that is, x1=x2, y1=y2, it can be obtained from the meaning of the question The slopes of straight lines MA and MB are greater than 0, that is, y1y2>0, contradictory;
Therefore the straight line BA...
……
Therefore, the equation of the straight line AB can be expressed as y=kx+2k (rounded down), or y=kx+(10/3)k, then the straight line AB always passes through the point (-10/3,0).
Xu Zongyun is very confident in the solution to this problem.
He can even be proud of it.
But before he could stand still for a few seconds, Xu Heng's words immediately brought him back to his original form.
"Is there a simpler way to solve the problem?"
puff-
Crit!
Break the defense!
"Don't tell me, you only considered this kind of problem-solving thinking?"
puff-
Crit*2!
Break defense *2!
"Looking at your expression, do you believe there is a second way to solve the problem?"
puff-
Crit*3!
Break defense *3! ! !
Xu Heng stared at Xu Zongyun, Xu Zongyun immediately shook his head, "No, no, brother! I didn't expect that! I just feel that this is already the simplest way of thinking, so, so..."
He didn't dare to look directly into Xu Heng's eyes.
He was depressed.
He clearly solved this question, and judging from what Xu Heng meant, he was obviously doing the right thing, but Xu Heng blamed himself so much.
His whole body is going to be torn apart.
At this moment, he lost all confidence in himself.
It turns out that only one way of solving problems is right, but it is also wrong.
I am so difficult! ! !
Xu Zongyun is like a child who made mistakes...
But he was obviously not wrong, but he still wanted to do this.
"Hey……"
He sighed resentfully.
But there was nothing he could do!
He finally understood the phrase "rules are made by the strong"!
Xu Heng, "Don't lower your head, read the question."
"This question can completely use the common formula of focal radius."
While talking, Xu Heng wrote.
"Equation [-] is the formula for the focal radius of an ellipse, Formula [-] is the formula for the focal radius of a hyperbola, and Formula [-] is the formula for the focal radius of a parabola. The point M coordinates (x, y), e is the eccentricity of the ellipse and the hyperbola, and a is the eccentricity of the ellipse and the hyperbola. The semi-major axis of the hyperbola is long, and p is the semi-radius of the parabola."
r1=a+ex,r2=a-ex
r1=|(ex+a)|, r2=|(ex-a)|
r=x+(p/2)
"Remember this formula, do it again, and the first question, you continue to see if there is an easier solution, I will give you half an hour."
After speaking, Xu Heng returned the test paper to Xu Zongyun.
Xu Zongyun took the test paper, not daring to waste a second, and immediately immersed himself in analysis and answers.
Xu Heng stood up, "I'll come back in half an hour."
After leaving the study, Xu Heng went to the bedroom.
Yue Pingting followed.
Xu Heng stretched his waist and climbed down, "My waist feels a little uncomfortable, rub it for me."
Yue Pingting, "!!!"
"What! Did you hurt your waist? Is it serious? Should we go to the hospital?"
Xu Heng rolled his eyes, "You girl... I usually bump into bumps, but I've never seen you so nervous!"
brush!
Yue Pingting blushed.
At this point, a small train should pass by.
Dirty...
Yue Pingting knelt beside Xu Heng and gently rubbed Xu Heng's back.
Xu Heng, "Heavier."
Yue Pingting curled her lips, "No, I'm afraid I'll break it for you."
Xu Heng, "No, try harder."
Yue Pingting, "I really tried too hard? Pay attention, if it hurts, tell me right away...` ~..."
But Xu Heng obviously enjoyed it, so why would he feel pain?
Half an hour passed by in a flash!
But for Xu Zongyun, this is simply suffering.
But at the same time, after he understood and knew how to do this problem, he was excited and excited!
Using Xu Heng's problem-solving ideas, Xu Zongyun suddenly became enlightened, and he felt that he had conquered the whole world.
A super sense of satisfaction arises spontaneously.
When Xu Heng came to the study.
Xu Zongyun held the test paper in both hands and handed it to Xu Heng.
Xu Heng checked.
Xu Zongyun considered this question and did it all over again.
B(c,b2/a)
AF=BF
a+c=b2/a
……
(e-2)(e+1)=0
So, e+2
……
Let ∠BFX=a, ∠BAF=b, ∠BFA=π-a, ∠ABF=ba
To prove that ∠BFA=2∠BAF, that is, π-a=2a...
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