in-20-27-a-write-each-equation-in-center-radius-form-b-find-the-coordinates-of-the-center-find-the-2

Question

In $20-27$ : a. Write each equation in center-radius form. b. Find the coordinates of the center. . Find the radius of the circle.
$$
x^{2}+y^{2}-2 x-2 y-7=0
$$

James Kiss · Accepted Answer

all right. In this question, we are given the equation X very plus y squared minus two X minus two Y minus seven equals zero. Um, and we need to put this into center radius forms off this. The equation were given. The first thing you should do is group things by, um, like, very well. So I&#x27;m in a group X squared minus two x together the positive X squared in a negative two x Similarly, do the positive y squared and negative two y in their own group. And I&#x27;m also gonna add the seven to the right hand side. So now we&#x27;re equal to seven instead of equal to zero. Um, you should be familiar with completing the square. Um, so in the first group, we can complete the square by adding one to it. You find that one by taking half of the negative to which is negative one and squaring it. That&#x27;s where you get the positive one. It&#x27;s so that we can write this as a perfect square, which you&#x27;ll see in a moment. We&#x27;ll do this for the Wiese&#x27;s. Well, we&#x27;re going to add one to the group, and again, we&#x27;re come up with this number one because we take the, um, negative too. Take half of it. That&#x27;s negative. One and square it. That&#x27;s positive One. And we&#x27;re so equal to seven. But this is an equation Will stay balanced on each side. If I added one to the left hand side of the equation twice. I have to stay balance and do this to the right as well. Now rewrite this equation. Our, um x group X minus one squared, ready as a perfect square by Nomura. These are equivalent to each other A few. Multiply it. X minus one by itself. You get expert minus two X plus one. Okay, Likewise. Why? Squared minus two y plus one is the same thing is why minus one squared and seven plus one plus one is nine. That is our answer to a. This now is in centre radius form. And from here we can see that the center was a six. Part of the question is at 11 and parts he asked for the re. Yes, And if this equation is equal to nine and the general in this form of the equation of a circle is equal to r squared, that radius must be three because three squared is nine

James Kiss · Answer

Alright. In this question, we are given the equation X squared plus y squared plus X minus three. Why one is to equal zero. But when a group our X&#x27;s and y&#x27;s together so that we can work towards getting this in Senate Radius form of the equation of a circle so x squared plus X gonna leave it a spot to complete the square. And why positive y squared minus three y Plus, we&#x27;re gonna complete the square of otherwise as well, and I&#x27;m gonna add the two to the right hand side. So we&#x27;re now equal to two. Let&#x27;s complete the square. Um, to complete this where for the exes, we get 1/4. How do we know it&#x27;s 1/4? The processes take half of the coefficient here, which is one half of that is 1/2 and then square 1/2 1 half squared is 1/4 will do that for the wise as well. Half of negative three is negative. Three halves. You square that and you get 9/4. Now to keep this equation balanced in some adding 1/4 and ninth force to the left hand side, I have to do this to the right hand side as well. So the padding 1/4 in adding the night before. So the right, All right. Now we want to rewrite thes, uh, groups into perfect square by no meals. Uh, so x plus, you&#x27;re the way you determine what this is going to be. Is this You&#x27;re kind of in between step. What do you get when you took 1/2 to square it? That&#x27;s a shortcut. Way to think about what it would be. And that would be 1/2. And so experts 1/2 squared is the same thing as X square plus X was 1/4. We do this for the wise as well. Half of negative three is negative. 3/2. So why ministry have square. And, um, we want to add all the values in the right hand side of the equation together. Think of this to as 8/4 so that we have a common denominator. Then we can add eight plus one plus nine, which is 18 4th and then that can be reduced. Think of that as 9/2. So So we&#x27;re equal tonight. Perhaps this now is the first answer to the took the question to write the Houthis given equation inside a radius form X plus 1/2 squared close. Why ministry Have squared equals 9/2 And so now we pull from this for part B the center of the circle. If we&#x27;re adding 1/2 to the X court to the X than our X coordinate is negative 1/2 If we&#x27;re adding subtracting three halfs of the wide, then our y according as positive three. House a negative 1/2 positive. Three halves is our center for the circle and we&#x27;re always equal to R squared. So what would our have to be equal to? In order to get nine halves, it would be the square root of nine Has you square the square root of Don&#x27;t have to get nine Hafs What? Simplify this a little bit. We can square root both the numerator and denominator separately. The scared of nine is three and will rationalize this by multiplying the numerator and denominator by square to to cause we&#x27;re not simplified with a radical and the denominator So multiply both the numerator by screw two in the denominator bias court to which makes the new denominator to so the radius must be three screwed to over to

James Kiss · Answer

are We are given the equation X squared plus y squared minus eight. Why equals zero? We need to complete the square on the left side so that we can get this into center radius form. There is only the X squared so there&#x27;s nothing to group here. But we will group the wise Why squared minus eight y so that we can complete the square with wise. How do we figure out what number goes here? To complete the square, you take what will be the middle term. Take half of it. So we have negative eight. Half of that is negative four and then you square it to get 16. And you have to add this to both sides of the equation. Now we can, um, essentially factor the wise. The one rented a perfect square binomial and that would be equal to y minus four square. A little shortcut on how to get there. It is the number that you&#x27;re taking hat. It is what you get when you take half so that you square. Um if you multiply y minus four by itself, you get the same thing. So these are equivalent and this is equal to 16 and now we are in our 600 radius form of the equation of circle. From this form, we can answer the rest of the questions. What is the center? What? It&#x27;s a radius. Well, since there&#x27;s nothing being ADDers attract the X. The X coordinate is zero for the center and the one record. It would be a positive force opposite sign of what we&#x27;re, um, doing to the why And the radius. This equation is always equal to R squared. So what square to 16 four. So this radius must be four.

Alice . · Answer

for this problem, we&#x27;re going to find the standard centrist and reform of the given equation of the circle. And then from that find the center and the radius. So for this one will need Thio complete the square and work to find the components X and Y on the left side. And then we&#x27;ll get the car one of the constant that we find along with that over to the right side. So we have two bunch are ex together and bunch or wives together. So we&#x27;ll have X group was two x plus some value. Ah, blank Plus why squared minus four? Why plus some value blank. Ah is equal to minus one because, well, scoot the constants of the right. So we&#x27;ll add one to complete the square for X square plus ticks plus one because to over +12 over two is one and one squared is one. Ah, for this one will do minus four. Divided by two is minus two minus two. Whole squared is for So that&#x27;s what we put there. So on the right side will have to add the same values we add one and we add for so because of that yet that the standards under standard equation of the circle his expose expose one whole squared plus why minus two whole squared is equal to four. So from that will get the center age comma K. So the center is equal to minus one comma, too. And the radius is equal. Well, we have our square from the equation is equal to four. If we take the square root of both sides will get the square root of four, which is equal to So that&#x27;s all the equation we can. That&#x27;s all the information we can describe from the equation.

Alice . · Answer

in this problem, we&#x27;re going to be finding wth e center standard form of this equation of a circle. So we&#x27;re given X squared plus y squared by his 25 is equal to zero. And since the Sanders for him is this ah, equation John Below. In order to transform it, we need to keep all the X&#x27;s and y&#x27;s on the left and the constant on the right. So to transform it all, do X squared plus y squared and then move the minus 25 to the right, making it a positive 25. So given this, the center of this would be of the form H comma K. And since there is no h r k in this equation, and that means that it was zero so the center of this equation would be zero comma zero. Then we go to the radius. Since 25 is R squared, we set our squared equal to 25. And then we do our is tthe e of 25. By taking the spirit of both sides and the reader 25 or at least the positive You&#x27;re 25 is five. So that would be the radius of the circle

James Kiss · Answer

All right, we are given the equation X squared plus y squared minus six x close to why minus six equals zero. And the first thing I want to do is, um, group the like variables together. So we&#x27;re gonna put our exes together and put our wise together. So x squared minus six x in a group. And, um, we got a positive life square in a positive to why? So put those in a group in, um, we&#x27;re gonna be equal to six because we&#x27;re just gonna add that six over. And there&#x27;s something called Completing the Square That&#x27;s gonna help us get to the centre radius form of the equation of a circle. And when we complete, the square will have X squared minus six x. And then we have to come up with 1/3 term that will allow us to write this as a perfect square by Tomio. Same to you with the wise. Okay, so I&#x27;m just putting little slot spots for us to figure out what never should go in there. So it&#x27;s illegal of six. How don&#x27;t come up with the number to complete the square here. It&#x27;s from the what will be the middle term here. Negative six if you take half of it, which is negative three and square it negative. Three squared is positive. Nine that it completes the square. That phrase comes from less. Allowing is to write. This now is a perfect square which will do in a moment if we do this with the wise. Now we take half of the middle term to which is one on ones where it is one. Now I&#x27;m adding the nine and adding the one to the left side of the equation. We have to state balance. So you have to do this to the right side of the equation as well. So we&#x27;ll add the nine and the one to the six. All right, so now the first group, um X squared minus six ex post nine could be rewritten as X minus three squared exponentially squared. If you multiply this out is the same thing as X squared minus six X plus nine. A little shortcut forgetting here is it is the number that we&#x27;re taking 1/2 of in order to square Is that number. We&#x27;ll do this for the wise as well. Same thing as a Y plus one squared. And if we add the 69 and one together, we get 16. Now we are in Senate Radius form of the equation of a circle That is your answer to part A. The second part of the question asked, Now that we have this form, what is the center? And then what is the radius? From this form? We can see that the center is at three negative warn opposite signs, and we&#x27;re always equal to R squared for the equation of a circle. So what squared is equal to 16 four? So three negative one is the center for is the radius.

Problem

In $20-27$ : a. Write each equation in center-rad…

Problem 21 Hard Difficulty

In $20-27$ : a. Write each equation in center-radius form. b. Find the coordinates of the center. . Find the radius of the circle.
$$
x^{2}+y^{2}-2 x-2 y-7=0
$$

Answer

(a) $(x-1)^{2}+(y-1)^{2}=9$
(b) $(1,1)$
(c) $3$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

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Michael J.

Absolute Value - Example 1

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(a) $(x-1)^{2}+(y-1)^{2}=9$(b) $(1,1)$(c) $3$

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Alayna H.

Kayleah T.

Michael J.

(a) $(x-1)^{2}+(y-1)^{2}=9$
(b) $(1,1)$
(c) $3$

Ann Xavier Gantert

Algebra 2 and Trigonometry