show-that-the-two-asymptotes-of-the-hyperbola-x2-y216-are-perpendicular-to-each-other-3

Name: show that the two asymptotes of the hyperbola x2 y216 are perpendicular to each other 3
Uploaded: 2020-08-09
Duration: 2 min 51 s
Channel: Numerade
Description: Show that the two asymptotes of the hyperbola $x^{2}-y^{2}=16$ are perpendicular to each other.

Question

Show that the two asymptotes of the hyperbola $x^{2}-y^{2}=16$ are perpendicular to each other.

Carrie Bain · Accepted Answer

we want to look at the happier Billa. It&#x27;s squared minus y squared equals sits stain. And they asked us to show that the SM totes are perpendicular to each other. The first thing we want to do is put this in our standard Fulham. So we divide by sits tain Yeah, that&#x27;s squared over sits stain minus y squared over six stain equals from one. Now our center is it 00 and discourages it stains for worse. So we can&#x27;t four units to the right, before units to the left and then under the Westport there&#x27;s a states takes we can&#x27;t four units. Ah, and four units Dan, It wouldn&#x27;t be drawn that about saying now the as some toads, Lau on top of the diagonals of that rectangle are actually the diagonals lounge, the s. And it&#x27;s now way went four units, uh, and four units to the right Notice the Wyler subsidizing rose. So that s and towed is why equals 4/4 ads. And that&#x27;s just like wills. It&#x27;s now the other Assam tote You go four units up four units left and so that asked him to Would be Why equals now the slope is for Ah, and then for laughs or negative for work. And so this ask them. Tote is y equals negative. It&#x27;s will the slow of, um, one of of that first sm tote is one, and the slope of the other Assen toad is negative ward. When when you have to slow jobs and you want to know if the lines are perpendicular, you find the product of their slopes. One tons negative born is negative. Woolen. When the product of the slopes is negative one, that means the lines are perpendicular, so the two slopes give a product of negative. Born first, those esteem toads are perpendicular.

Sriram Soundarrajan · Answer

Hello. You are never going to solve our problem. Number 15 here doesn&#x27;t bring us in our call. This hyper Bhola is a Cuban, but hi purple eyes gonna bake, of course, but he s square minus my square by square called Cooper for standard the you&#x27;re a square A could be throw standard that will be going through Yes. Oh, my b by year in the U. S. Here, plus or minus, year by year in tow. Learn if one day doing at the very cold wave at the other end while you go to minus six year, there&#x27;s no I&#x27;m gonna go to one. I am Greek going through mine, isn&#x27;t you? Both are happening that direct all their sloping big toe minus like weren&#x27;t indoor My toughened. You do minus our Yes, there are particular. Thank you.

Suman Saurav Thakur · Answer

they said, Remember, 62 we have you in the hyper bola excess squad by four minus y squared. But it be a spotty called one is given Fine, Be so that seems towards our perpendicular to each other So isn&#x27;t or should have been x equal to minus me by X and B by X. In this case, a symptoms will be Why call toe minus B by two X. I call Toby by two weeks. So these are the slopes off the same towers for this has imposed to be perpendicular minus B by two in tow, be by two. Should be minus one because multiplication of store slope is minus one for the life too perpendicular. So this will cancel out be a square will be equal toe for so people were equal to two. Okay, so who is the answer? Well, thank you

Farnood Ensan · Answer

and this problem will give it this following equation which is the on general format of her book. Every asked for what dollars of a and b are the acid totes a paragraph perpendicular to one another. So if this is the general shape of a hyper bowl, uh, you said to find this ankle boots Vienna, we want it to be perpendicular or 90 decrease. Well, I think about it when A and B are both you goto Juan. In the regular format, you have to falling. You have, like, this left side on the right side, and then the ass enters are technically perpendicular because best I seven tree each assam toe splits the angle creative I t x and the y axis into half or 45 degrees. Therefore, it will be 45. This will be 45 overall will be perpendicular for 90 degrees. So if a because to be then, um, little house perpendicular, hasn&#x27;t it? And while you sat again again, this look at some photos are positive. Make it&#x27;d be over a FDA close to eight, then Positive. Negative. You&#x27;re OK is positive. Negative one. I mean, no meant This still surprises naked form, you will have perpendicular angles. Now let&#x27;s look at our cases. If a is figured and B if a speaker don&#x27;t be every will have, its slopes are positively could be over a and he&#x27;s less than a which is less than what and they get. Hunt couldn&#x27;t negative. Therefore, our ass centers will look something more like this, and we can see that the angles are not perpendicular. Same did the officer. If he&#x27;s Gourgeon, Hey and have a craft will look more acute. More like this and again, not her convicted. It&#x27;s the only case to get perpendicular angles after the passage of meat is a vehicle sabih and take a few positive. It could be a few goes, possess negative B and are not equal to zero.

Bobby Barnes · Answer

we want to show that the lines. Why is it reminded? Be over eight tones X Are these like acid tubs of hyper Bhola squared over a squared minus y squared over peace. Where is he? So what I would have had and did to start waas rewrite the equation just in terms of why which we end it with this square root with the plus or minus. So the reason why I didn&#x27;t pull off the B squared is because if we don&#x27;t know if he is possible negative and we would have to have this absolute value and I just don&#x27;t have toe right absolute value every now and then. So, uh, just kind of keep that in mind If you do pull it out. When you&#x27;re writing this, there needs to be absolute value of being on the outside. Uh, but if we want to show that those are the slight ass because what we need to show is that this function here, minus one of those lines is equal to zero when we take a limit SX a purchase infinity. So Ah, and I&#x27;m gonna claim that e positive square root of positive line and the negative square root cause with the negative life. So let&#x27;s go ahead and go through how the take these limits. So you might remember from the chapter when we talked about infinite limits, that the technique we should use for this is to multiply by conscience. So let&#x27;s go ahead and do that, because by multiplying by the contra get we get rid of that square root. And remember, the congregate is just We take the middle term and make it the opposite side. So it&#x27;ll be plus, as opposed to mites and they remember any time multiply. We also have to divide by the conflict because we can&#x27;t multiply by anything other than one. Okay, so we end up with that&#x27;s here now when we go ahead and multiply out, remember, that&#x27;s just the difference Squares. So we&#x27;re going to be left with. Well, the square roots will end up. Just cancel no, essentially And what be squared times X word over a squared minus one and then minus B A. But those were X squared and then all over our conscious yet still peace word X squared over a square mile swim square rooted plus B for her a X No notice. If we were to distribute this b squared, then we end up with a positive p X squared for a squared. So that ends up counseling out with that there and we&#x27;re going to be left with the numerator. Just be square or a negative piece works a lot of negative b squared and then all over our conscious kit again. B squared times, expert of his bird, minus one square rooted must be over a X Now, If we were to take the derivative of this directly, you might notice that will end up with infinity. Plus, I&#x27;m going to say be a infinity like that. And the reason why I&#x27;m saying be over a is well, if be divided by its negative, we&#x27;re gonna end up with unity. My symphony and I have no idea what that means. So just to kind of get around that what we&#x27;re going to do instead, it&#x27;s first multiply the top and bottom of this by one of her ex. Before we actually applied the limit. So doubt doing this, we&#x27;ll have the limit as experts pity of negative e squared over X all over it. Remember when we pulled that one over X into the square root. We have to square it. So that&#x27;s why it will cancel out with the X squared that we have in there. So be square will be won over a squared minus one over X word square root and then just plus B over. And I noticed when we take the limit of this well, the new mayor goes to zero. That there goes to zero and we&#x27;re going to be left with zero over the square root of B squared over a squared plus B over a, which is zero so that their shows that be over a X is one of these slant pass symptoms. Now, for this next one here, we can go ahead and follow the same steps. So first noticed that these two negatives there counts and we can go ahead and rewrite it with the B A or B, divided by a X in front and in follow the same steps. So just not to kind of boreal with algebra again. I went ahead and did this beforehand. So in this first up here, just like we did before, we multiplied by congregate and after that everything would simplify down to just be squared times one of her ex or be square over contra git. And what we&#x27;re going to be forced to do once again is multiplied by one of her ex. And we end up with this equation here. And then again, we just go ahead and take the limit as excuse infinity. So the numerator goes to zero. This part of the square root goes to zero, and we&#x27;re going to be left with zero over eat over a plus. He&#x27;s where, over a squared swear rooted, which again is a cigarette so that their shows that the other line is also a slant acid, too.

Rakesh Kumar Sharma · Answer

they wish along the likable a demon. In this question, eyes y squared away full wherever sexists were. Very 16. Until I have that additional them, I focus on AIDS to form yet and the easiest route for relinquishing out that I support you every because first pregnancy a baby because this guy paralyzed parts of Texas along by exit, and every that mission will be less for messing might be the next provision. So I really because this is a school these forward back. So that would mean that&#x27;s why that&#x27;s expected so that just being out of the party original best.

Problem

(a) Verify that the point $P(6,4 \sqrt{3})$ lies …

Problem 37 Medium Difficulty

Show that the two asymptotes of the hyperbola $x^{2}-y^{2}=16$ are perpendicular to each other.

Answer

$m, m_{2}=-1$

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$m, m_{2}=-1$

Precalculus With Unit-Circle Trigonometry

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Anna Marie V.

Megan C.

Kristen K.

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David Cohen, Theodore B. Lee, David SklarPrecalculus With Unit-Circle Trigonometry

Grace H.

Anna Marie V.

Megan C.

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David Cohen, Theodore B. Lee, David Sklar

Precalculus With Unit-Circle Trigonometry