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Given the following information 7 =1 findthe equation for one of the asymptotes_ Do not include spaces to increase the chance auto grade will workQuestion 48ptsGive...

Question

Given the following information 7 =1 findthe equation for one of the asymptotes_ Do not include spaces to increase the chance auto grade will workQuestion 48ptsGiven the following information=],the hyperbola opens up/down:TrueFalseQuestion 58pfGiven the following informaticnI,fni thecocrdinates ofthe vartices:

Given the following information 7 =1 findthe equation for one of the asymptotes_ Do not include spaces to increase the chance auto grade will work Question 4 8pts Given the following information =],the hyperbola opens up/down: True False Question 5 8pf Given the following informaticn I,fni thecocrdinates ofthe vartices:



Answers

Determine whether the statement is true or false. Justify your answer. If the asymptotes of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1,$ where $a, b>0$

Way Have problem number 30. The parable the hyper bola y Squire by a square minus. Access quite equal to one has an I seem taught the lines. Okay, So, uh, when we need to find the same thought, we should always plug in it or replace one with zero. So after replacing one with zero will be getting wa square by square minus x squared equal to zero. Which means why, Squire by a square, equal toe access squired by cross multiplication. Why square will be equal toe is quite x square. So why would we call toe Plus minus is quite access square, which means it's in totes is essential. Sir, Why I called toe plus minus a X. So this is the This should be the same total. But we have been given the simple article toe plus minus x by a So this is not the simple. So it is false. Thank you so much

Uh The quick answer to this is uh this is a true statement um and to kind of get into a long explanation is to think about what needs to happen um In the order for you to have a some toots at least in the form that we like to be perpendicular to each other. So the whole, I guess the premise of this would be what needs to be true in order for this to be a right angle. Well what needs to be true is that the slopes of B over A plus and minus? Um Yeah, I just think about what's the only values for A. And B. That they can be perpendicular. Well, let's think of it this way is if we have positively over A. And then you want it to be perpendicular to be negative B over A. Remember in order to be perpendicular, they need to be negative reciprocal. It's well, the only way that this can happen is if A equals I guess negative B. If we think about the reciprocal as A becomes B. And then B becomes A. Um So yeah, I know this is not really a proof. Um But it's more of a thought process as to why it needs to be true. And the only way for you to get perpendicular assume Totes is if the negative reciprocal, and that can only happen is if A equals B. And A negative B. I mean, you can attach the negative to either one of these things doesn't matter. Um So that is a true statement what they said about A equaling B.

So this problem is asking about why equals one over X squared minus four. So a vertical ascent tote occurs when you have a number divided by zero, that means you have vertical ascent toe. So um we already have a number in our numerator. It's just one. I don't have any excess in my numerator. Um but my denominator let's set that equal to zero and see what happens. X squared minus four equals zero at four to both sides. X squared equals four. Take the square root. Don't forget that when you take the square you need to put x equals plus or -2. So if I have one of two, for example, that would be 1/2 squared minus four, Which is one over a zero. Which gives me a vertical ascent up. If I do the same thing at negative 21 over negative two squared minus four is equal to one over negative two squared is four for minus four is zero. So that's another vertical ass into it. Again, it's when you have a number divided by zero, when you plug in that X value. So there are two vertical as um, totes. There is one at X equals two, And there's another one at x equals -2. So this claim is true. There are two vertical ascent oats for this function.

Okay, so we're giving the function here. F of X is equal to three x squared plus B squared, all divided by X squared, plus a square plus a plus A. It's morning up, plus a squared. Right. Um, so were asked to find in the vertical, um, And while to find all the essentials. So a vertical assam told a vertical Assam talk is well, where the denominator is equal to zero in the numerator is not equals zero. There. Okay, well, what values of eso again? The variable here is X Right and be can be regarded as constants. But what is over? A set X squared plus a squared equal to zero then. Well, what values of X make that zero. Well, nothing. Right, Because X squared is never zero. I don't care what X is right. Excess squared is never zero. And likewise a squared is never zero right. We know a is some constant. I don't know what it is, but it doesn't matter if a is positive or negative. I'm squaring it and I'm spring some number squared, which is passing positive, plus some other number squared. That has to be positive. Um, can never be equal to zero. Well, I'm saying that, but I'm thinking Wait a minute. If X was zero, right? If you play if what is while you plug in zero for X? Um, you know, a squared. I think a should be regarded as a non zero constant. Because if a zero that is not even involved in our so I mean, if X was zero, let's say then. And if a was zero, well, then the nominator is equal to zero. Right? Um is the numerator equal to zero? Well, if b wasn't zero, so I think the answer they want here is no vertical asking. I'm gonna put none with maybe a little asterisk here, because again, I'm not given the answers. I'm not sure what answer the book wants here. Um, but if x I mean, if X was zero if X equals zero if this if X equals zero, um was a brick lasting told Well, that means that a would also have to equal zero. So a what also f t equals zero and be will be could not be zero because it be was there all then we'd have So, uh, I don't think this financial they want. I think they want the answer. None. Okay, um but just if this was true, then we would, I believe yes. Have a vehicle hasn't told. But what do you think seeing is that? This can never be zero. Right? Um, unless a 10 what a was zero, then be canopy zero, because then you would have some non zero constant over divided by zero. And then yes, he would have a critical as I'm told, um, at actually zero. But I don't believe that the answer they want, but, um, it's a little like that. Okay, so we're gonna go with none, because the denominator can never be zero, because we're gonna assume that is not gonna be zero on. Why would they even have a So Okay, I am ran. But enough about that. But we're gonna go with no ver glass and votes for this function. How about the horizontal? Assen told Well, what we notice. We noticed that the degree of the numerator is the same as the degree of the denominator. So therefore, our horizontal ask pope is just the ratio of the leading coefficients with three of the one. So it's a horse. I don't lying. So it's why equals and why equals three. Why? Cause three is our horizontal? Asked that I take care.


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