Show alLyour work for lulLcrcdits_Check your fnaLanswcn1. Identify the type of conic section, find the vertices, foci (asymptotes if exist) and sketch the graph: xl...

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$25 x^{2}-9 y^{2}+100 x-54 y+10=0$$

The focus points are zero plus or minus groups of two. This tells us see ISS square root off too. This is a hyper paella. The focus points are on the y axis, which means it's why square minus X square, the S and toads are Why equals to post Remind us one time sex. So be over A It's what we also know that too which is square off see will be a score post be square So then we get B is the same s A which is one And remember, focus points are why excess So we have y squared minus x square. So then the answer is why square over B square which is one minus X square over a square which is also one equals to what?

So in this problem were given This is the information double your given about a a high purple and we're else to figure out the equation for the hyperbole and in standard for So, um, I'm first gonna look here at the full cut. Um, since both of these points are in the white access, that means that's that means that the X axis is the total access. And this information will tell us the general shape of the equation. So since access the local access, that means the term with eggs is going to go first. And first term always has to numerator case cleared minus nice comes wife's cleared. And this is always has been memory to be squared the second, um and this will be equal to one. So we already know the shape of the equation and extended what we just need to figure out a square and beastly. So that's when we use this other piece of information along with the fact that we know that since we know he this is the equation for the hyperbole, we know that it's Assam toots are going to have, um they're going to look like this. Why you want to Pleasant, Linus. A over B, Times X. Great. So now we just need to compare it to what? We actually have another. Won't be able to tell a ce who a is and who be it. All right. So they will be this number on top A will be one big asses in a married er. That means it is squib motive three. Awesome. So we have a we have be So we jump up, we just need to plug it in here. But we need a squared and B squared. So squaring won. We have won squaring the square root of three. We get three, right? So now we just put together the secretion This is all you and this value. So in the empty house X squared over a squared Who is fun? So we don't need to write that we can just write X squared nine is why squared over peace grade? Who is three? We really right there. And that's equal to one so good looks. So this is, um, the equation that we are looking for

Mhm. The transfers axis of this hyperba is vertical. Hence Echoes. The script would have won the trust one P equals the square root of 15, and C equals the square root of one plus 15 ventricles. For Hence the verses of this hyperba zero Plus or -1, the full size of this hyperba zero plus or -4. And the salesman told of this hyperba of Y equals class of minors over B. X. That she calls Plus Minors. One over the square root of 15. Yeah. Which also echoes plus on minors. The square root of 15/15 x. In this graph, the two green curve on the graph of the hyperba, the two right doubted nines, the asthma told and these two yellow points, uh the fulsome.

First we can rewrite this, acquiring us 130 and 44 x squared. Last 860 flax mas some constant number such that this is a perfect square. And this number should be 36 square minus 25 y squared minus 100 wide miners. A constant number such that this is a perfect square. And this number should be 10 squared and the right hand side is to sell them For him. Very and four special miners. 36 square. And then plus sorry We shall plus 36 squared. Then miners 10 square enhance this becomes 12 x -36 plus 36 squared miners five Y plus 10 squared. He calls 3000 and 600 with vehicles 60 square amazon. We can divide Both sides by 60 squares. And it it becomes express three squared Over five squared. My nurse y plus two squared Over 12 squared equals what. And from this we know that eight equals 5. The he calls 12. And see because 13 which is the square root of a squared plus B squared. And send her. It's K. Because my nurse three and miners too show that vortices of this Hyperba Yes, eggs plus minors. A. Okay. Articles -3 Something -5. My arms too. The full size yes. H plus or minus C. Okay retreat calls my nursery Class of minors 13 Mourners to And the as mom told us why or a nurse. K eagles press on minors be over eight X minus H. Hence the asthma victorious. Why? Plus two equals plus are minors 12/5 times express three.