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Identify and sketch the graph of each relation.$x^{2}=25+y^{2}$...

Question

Identify and sketch the graph of each relation.$x^{2}=25+y^{2}$

Identify and sketch the graph of each relation. $x^{2}=25+y^{2}$



Answers

Graph each equation.
$$
x=y^{2}-14 y+25
$$

So according to the questions data, we have exist. Quit minus full of Isis. Two weeks Last win before by Wendy Ford. Why equals true? 51? Okay, Toe again. Hamas said told us all about curry. Toho Marie Posse, Argentina X plus one Go. Hold square minus one minus. Dubai minus six. Car holds. Quit Bless 36 to get a letter score. Romney basically sold out care which will be a question for everyone. Okay, so you Haagen I'm JK Toe Yokohama arepas X minus X plus one whole square minus two by minus six. Car hold square or Yeah, Jack Amar Bus. So lucky. But Robert, we take the constant on the right hand side. So yeah, I got X plus one cool squared, Divided by 16 Or your house Agam too comical. Danto Two squares. Ho Jagger. That will be four by minus three. Whole squared, divided by 16 is Enquist one. So this will be four or hear money. Pasok parabolas. Erica Express One car. Whole square, divided by 16 miners. Why minus streak A whole squared. Divided by four equals to one. Soc parable occurred. Your graph armory plot connects with This is the graph. The answer. Thank you

So according to their data that has been given to US media reinstall equation tomar pass operate I got X minus 25 is equals toe 20 by square minus 40 by 20 commonly calling it to ya Jackal. Madiba's Why square minus do why or you got X minus 20. Fight of a miss A perfect square game for mega convert Cannot charge two years ago as we know that a minus week a whole square is equal to a square plus B squared minus twice a B to get some perfect square k his object and what can on child two year Hominy passenger train people to apply to buy. Why minus one The whole square minus cuchi Hopper B squared Joy war Yet that this will be minus 20. And he I got X minus 20. Fight for us off putting about Iago. My purpose X minus five is equals 20. Why? Minus one car holds great. So this is the graph that can be drawn according to the giving data. So that's the answer. Thank you.

So in this problem, we're being asked to analyse and graph given equation. Well, the first thing I'm going to do is I want my equation to be set equal toe one because it looks like one of our comics. So what I'm gonna do is I'm gonna divide both sides or every term river in this equation by 100. Well, 25 divided by 100 is 14 So we'll have X squared over four for why squared over 100 is going to reduce the Y squared over 25. And 100 divided by 100 is equal to one. So now I know that this is the equation for in the lips. All right, well, now we need to center. Well, because our new Meridor's air just x square than y squared the center for the Selous will be The origin will be at the order paired 00 All right, now we have to go ahead and find our vergis ease. While Harvard this ease are found, five taking are a value or a squared is equal to, um for in this picture are sorry underneath our y squared terms. So a square will be equal to 25. Well, that means a could be plus or minus five, which means that it's going to be five minutes away. Now, here's the one thing we have to take care pay attention to because I've heard this eases underneath our y axis. That means our major axis is R Y axis. So our ver theses air going to affect the Y value compared to the center so are to further seas are going to be zero positive five because it could go up five or it could be zero negative five. Next, we need to find our folk I Well, in order to find our folk, I we need to find our see value will remember to find our see value, we're gonna have our formula. C squared is equal to a squared minus B squared Well, a square. This 25 and be square. This four and 25 minus four is 21 so C squared is equal to 21 which means C is equal to plus or minus 3 21 And again these will go along with our major access. So our folk I are going to be zero negative route 21 as well as zero positive 21. And the last thing we confined our the minor access and points. So I'm gonna play here minor access and points and we get these using RB value. Well, we know that B squared is equal before, so B is equal to plus or minus two and again our mind their access in this case is our X axis. So are two minor acts. Some points will be negative to zero as well as positive 20 Now we can go ahead and graft this So if I set up a graph here 123451234512345 2345 Here's our Y axis and our X axis. Well, first thing we had our center was at the origin are further sees were at 05 and zero negative five. So here 05 and we have zero negative five our mind. Their acts of some points were at 0 to 0 and negative to zero. So here are minor access and points on our folk. I were at zero and Route 21 0 and negative route 21/21 is in between four and five. So these will be in between negative for five right in here. But remember, they're gonna fall inside our lips. So now we can draw our lips here and now we've craft our equation.

Okay, We're going to sketch the graph of I per bleh This particular equation Ah, has a y squared over 25 minus X squared over 49 equals to one one of the standard form equations of hyperbole. A has the y squared over B squared minus X squared over a squared equals one. And this mimics our standard form. So that's how we know it is. I per Bollegraf s. So what we're going to start with is taking my 25 which is B squared. So be is plus or minus five and taking our A squared, which is 49 and that makes a plus or minus seven. Okay, because the Y squared leads off in the front of this equation. That means our purple is gonna open up and down along the y axis. So we'll take our plus or minus five as the B values and I'll plot them on my why access as points and I'm gonna use the plus or minus seven toe help sketch the graph of my hyper bola. I'm going to go out to seven on the right and two negative seven and I'm going to go up to the five and put a dot and down to negative five and put dots. And what you'll see me doing is just making a quick rectangle between all of those dots. And when I'm using the rectangle four is to sketch Assam tubes. The ASEM hopes will be from corner to corner across the diagonal. And so we have a nascent ope like this and an ass in tope like this. And what we're able to do with these ass and hopes is show how the graph hugs along the ascent hopes toe wear the U of the hyperbole that is opening up will go along this ascent Oh, pretty wide on both sides and on the bottom as well Open toward the acid dopes kind of hugging along these ass on tips. Okay, Now, if you were to get a sketch of this in a calculator or any type of computer program, you would not see the red box or the red lines that I have here, but they're good to help us sketch the graft by hands. This equation why squared over 25 minus X squared over 49 equals one Is this sketch of the hyper bola


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