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Consicer thie quadratic [OTHQ6r) =ri+on2+13. for the values ( = 4, =2 ad ( = 3For each value of €, complete the square AId determine the siguature o Q). (6) U...

Question

Consicer thie quadratic [OTHQ6r) =ri+on2+13. for the values ( = 4, =2 ad ( = 3For each value of €, complete the square AId determine the siguature o Q). (6) Use this to determine what type of conic section is dlelined by this Q(). For each value of &, COMpte the eigeudecomposition of the corresponding symmetric Hrix A= (d) Use the eigenvalues to determine the signature of Q(r) , verifying that YOu obtain the SAIHO result a5 when VOu completed the square

Consicer thie quadratic [OTH Q6r) =ri+on2+13. for the values ( = 4, =2 ad ( = 3 For each value of €, complete the square AId determine the siguature o Q). (6) Use this to determine what type of conic section is dlelined by this Q(). For each value of &, COMpte the eigeudecomposition of the corresponding symmetric Hrix A= (d) Use the eigenvalues to determine the signature of Q(r) , verifying that YOu obtain the SAIHO result a5 when VOu completed the square



Answers

The sum of the squares of the eccentricities of the conics $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ and $\frac{x^{2}}{4}-\frac{y^{2}}{3}=1$ is (a) 2 (b) $\sqrt{2}$ (c) $\frac{\sqrt{7}}{\sqrt{3}}$ (d) $\sqrt{7}$

It is question here we recall about question I X Square plus B x y plus c y square plus the X plus e y plus f e coaches zero If we consider the quantity d denoted by the cornice discriminate defined by the B squared minus four. I see if this quantity in here smaller than zero and then we get this one will be the lips credit. And so again, this one will be the hip popular, eh? Coaches only began that popular in this question were given the two X square minus three X y plus the five Y square minus four equal to zero. Here we can identify. This one will be the A B and the sea. They found the discriminatory equal to the B square will be the night minus far, I say four times, two times five girly. This one will be smaller than zero. Therefore, we have in this case now that we should listen. Some result in on lips here. And that's for me. The answer for this question

In this question, we record of other discriminate. Do you notify the day ICO to the B square minus four. I see on the equation on the I X square plus b x y plus See why square plus the X plus e y plus f e coaches around Now if the d here if smaller dancer on then we have the lips on the circle E lived on the circle here then we have the day here created than zero We have the single with a hip popular Yeah, but LA and the day exactly equal to the zero. And then we have this one will be the Papua on now discussion here were given the question I'm the far X square plus five x y plus seven y square, including 24 Yeah, we can identify This one will be that guy. See, this one will be on it will apply the formula we can compute now the discrimination the equal to the be square with the five square minus four times a time. See, you can equal to the 25 minus. This one will be the, uh 16 times seven because you won 12. So this is clearly smaller than zero. Therefore, we are in this case now and we can conclude that this one you shouldn't gander and lips. Oh, so cool on. That's gonna be the answer for this question. Yeah.

So we have. The equation for expert was 20 by y squared minus 24 x past wanted to. The wife has 561 called zero. We take notice that this part this letter a us upon extraction this letter b when it's it's positive, but same sign. But it has different that equal but also it considered as a lips. So here, the first to do is tow the group The first, the same by Arab also help for expert minus 24 x last 25 white skirt that started with do I. Then he he test forced the 561 toe other side of the equation. So it is equals toe. Okay, keep 561. And here the next step is to factor out all month. Um, on both different parable. So we have here we have about her out the war. So we have poor attempt. A quantity expert. Yeah, minus six. I believe the space for the completing the square here. So we have Plus we factor out here 25. I'm so I squared last a night Sequels toe negative 61 then used completing the square so first with by the middle term by two. After the body hit on the number of coefficient, that is, he goes to three. When me spirit that three squared that is equals to nine. So I hereby positive nine her with have X When we squared X, we get the ex creditor so it satisfies the They know my script perfect for trying Normal. So here we added nine with poor support times nine that singles to 36. So at also in the other side of the equation by 36 domestic violence here with about 10 by two Remember the middle term but the sickles toe to a p off the final Mel from B squared last two a B plus B squared. This is a perpetrator No mill. So it will look a that me This should be the factor Farms From here we have to a be So we have here with the body weight. Oh, so we get a and the reason we have five y So let there be peace pipe. So you have toe skirted. So we have 25 here and this one will be your wife is good, she said Status space The perfect score trying normal. So we have the 25 year. So we are 25 times 25 30 seconds to 625. So also add to the other side of it. We should That that is 625. Now we have to factor or have to use this. We have now four times the quantity X minus tree scrag plus 25. I am still quantity. Why plus five squared that is equals to here. We have to add this the I get the 561 plus 36 last 625 that is equals to 100. So make this in standard form with the by both sides by equation off 100 to have X minus tree slurred over 25 plus why plus five squared over four that if she goes to one, here is the standard form of the Ellipse. So we have the standard form of X minus h squared over a skirt to us. Why am I an escape screwed over b skirt That is, she calls toe one. So the a east the major axis off ellipse and be that iss minor artist upper lip since it on. Except so the grapple looked like this. It's my major access alongside with vertical horizontal axis. Or exactly so we have here. The letter a is called to squared off 25 30 singles five we sickles toe to you can determine the sees value with using the formal of thescore that singles too. A sward mindless we skirt. So see, it's equals 25 minus four that this goes toe squared off 21. So we have, uh, center. We have also determine the age, which is Sequels to three. Casey goes to negative I So here we have center off an ellipse. But he says, expressed as h. A Berkey, do you have saying there are the negative? Fine, that is Okay it along the x axis, the parabola. So yeah, each less a h minus a Mhm Yes, you see on the map. So w off a that comes to five. So we have h is equal Street three perspective that is Singles eight and negative Pride Also age 30 Sequels to treat my nose by She goes negative de negative by Look out from H is three. My nose five this negative toe. So we have both sides. Jose is from the H past Eve. Negative c it thing. So we have the age status equals toe three. That's my nose skirt. 21 and decades is negative type Just only have the major axes it is supposed to do. A so two times five equals 10 is the major axis in our arses, which is Toby? We have Are you free? That is equal to two so two times. So that is equal to four. So this is the group of the equation of ANA lives for export just 25 squared minus 24 x just wanted people de y plus by 1 61 that equals to zero.

In the question we way We record about the equation a x square plus B x y plus c y square plus the X plus e y plus f equals zero And then we consider the discriminating d the fight by the B squared minus for a C. If we have the d here smaller than zero, then we get the Ellipse square then So we got the hip Papua exactly equals zero. And then we get it will be the Papua in this question here were given the two x choir minus eight x y plus three y square minus four equal to zero. Yeah, we can identify This one will be the I be and the sea. Therefore, we computer discrimination d ego during the B squared with the 64 minus four A c so four times two times three getting into the 24. So this isn't currently greater than zero. And when is greater than zero we have in the second case? Yeah, So we get this on your vida. Hey, purple A and asking me the answer for this question Here


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