in-20-27-a-write-each-equation-in-center-radius-form-b-find-the-coordinates-of-the-center-find-the-3

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.
$$
x^{2}+y^{2}+2 x-4 y+1=0
$$

Alice . · Accepted 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.

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.

James Kiss · 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

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

Alice . · Answer

Hello. So the point of this problem is to convert the general equation of a circle into the standard certain center standard of so we&#x27;re giving this equation and we&#x27;re trying to convert it into the form that trump alot. So in order to do that, we want to keep all our variables to the left and the mover Constance to the right. The most that we can do for now is try to complete the square with our variables, and then whenever we get Constance will move them. Our cause is that fall out of the brackets will move them to the right. So we have currently X squared plus 10 X. I&#x27;m also grouping them by the type of variables. That&#x27;s easier to complete the square, plus some value plus why squared minus five y plus some value we&#x27;ll complete. The square is equal to 32. So in order to complete the square with this I&#x27;ll do 10. Divided by two is 5 25 is what we add on. And then for this one, we do minus five, divided by two whole squared is 25 over before. So, taking this information, we moved down. We do X plus five well squared. Plus why minus five over too cool squared. Oh, I forgot to add on my Constance. I apologize. I should have added 25 to the right side and added 25 over for as well. So now that we deal with those constants, we can have it&#x27;ll be 57 plus 25 over four. So that will make the center of this equal to a minus five comma five Ever do? No. And the race would be equal to what we have are squared is equal to 57 plus 25 over four. If he wanted to turn that into a, uh, another bigger fraction. We get 2 to 8 over four, equal to 57 over four. And if we added that to 25 we get, um 2 53 over four. So the are in the situation would be d square root of 2 53 over too. So that&#x27;s the information we can get from this equation.

Problem

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

Problem 22 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.
$$
x^{2}+y^{2}+2 x-4 y+1=0
$$

Answer

(a) $(x+1)^{2}+(y-2)^{2}=4$
(b) $(-1,2)$
(c) $2$

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Anna Marie V.

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(a) $(x+1)^{2}+(y-2)^{2}=4$(b) $(-1,2)$(c) $2$

Algebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Michael J.

(a) $(x+1)^{2}+(y-2)^{2}=4$
(b) $(-1,2)$
(c) $2$

Ann Xavier Gantert

Algebra 2 and Trigonometry