let-h-k-be-the-center-and-r-the-radius-of-the-circle-whose-equation-is-x22-xy2-4-y10-what-is-the-val

Question

Let $(h, k)$ be the center and $r$ the radius of the circle whose
equation is $x^{2}+2 x+y^{2}-4 y+1=0 .$ What is the value of $h+k+$
$r ?$
$$\begin{array}{l}{	ext { (A) } 1} \ {	ext { (B) } 2} \ {	ext { (C) } 3} \ {	ext { (D) } 4}\end{array}$$

Lily An · Accepted Answer

cancer. We have let H Kama K b the centre and they&#x27;re radius of the circle. True&#x27;s equation as X squared plus two experts y squared minus four y plus one is equal to zero. What is the value of H plus? Que was r So we know that our standard equation for a circle this X minus h squared, Let&#x27;s fly minus case squared is equal to R squared. So we need to get this equation right here to model this one a little bit more closely. So we know that the first thing that we want to do is to move the one over to the other side, at which point we&#x27;re gonna have X squared was too X. What&#x27;s Y squared? Minus four Y is equal to negative one from here. We want to complete the square, complete the square, so we&#x27;re going to need to break it up into the ex components and the Y components. So for completing the square here, well, we need to do is take the B value, divide that by two, square it and add that to both sides. So the value here is to the to divide by two. Is one one square to stole one. So we&#x27;re going to be adding one to both sides. So now we&#x27;ve got X squared plus two x plus one plus y squared minus four Y is equal to zero. We&#x27;re gonna go ahead and do the same thing for the why the negative for over two squared is going to be four positive force. We&#x27;re going toe at Fort. Both sides get X squared plus two x plus one. That&#x27;s why squared minus four y plus four is equal to four. So then, from here now, these two components right here, our factory ble. So we&#x27;re going to go ahead and factor that and get X plus one squared. Plus why minus two squared is equal to four. From here, we know our H Kama K is our center point. So we know our center point is negative. One common, too. And our radius is going to be the square root of whatever values on the right side. So that should be two of her. Adding negative one plus two plus two that should give us three to A C is air correct Answer

Ernest Castorena · Answer

Okay. This time they give us the equation. Export plus y squared. Let&#x27;s see. Minus for X minus one is he went in there. Well, that may rearrange a list to make it a bit easier towards and all right, why squared his linemen? Sarah Square? So we see. We don&#x27;t need to complete the square for that. What we do for the X. So let&#x27;s see Divide that by two will get negative two squared and that it&#x27;s a little science before it&#x27;s all said. And so the equivalent equation and still the same as the previous one. Now I see. And I did that. Something extent was easily factor is the next month. Okay, so I&#x27;ve seen This is definitely the fact there because we&#x27;ll get an X squared minus trucks minus two looks. What&#x27;s where. This is our standard for him, it could be righted a little bit, so it&#x27;s easier for us to see the do much information. Plus why my serious when people see the square square and then we think that center it&#x27;s X coordinates means of practice connects. That&#x27;s like ordinates going to trust the boy as radius is being squared on the right and sent to the Senate areas to calm a zero on the radius. Is this where you five awesome.

Ernest Castorena · Answer

this big of a secret for extra. That&#x27;s for that C minus 12 minus four away. My six days equals is here and what We could divide both sides of the equation by for to get excellent plus y squared minus the X minus. Swine, my ass. Let&#x27;s see, Very over two is equal to zero, and now we could rearrange it. Since Edition is community, we have exported three x The class y squared minus one is equal to the house. Okay, now we can divide its coalition by to square it on. It&#x27;s about science plus 9/4 plus 9/4. And in the next episode of FACTORED as Let&#x27;s see X minus 3/2. Quick. Is that good? Expand. It expired and then minus they over two X minus three over directs that exclusive report. And over here, the coefficient We&#x27;re gonna be looking at negative one divided by t on half native but square. It&#x27;s a full sense we&#x27;ll get plus one the worst plus before. So now this tractor as a Y minus one. We&#x27;re and on the right hand side Well, this is a 6/4. So what? We have is a 16 hours before, which is just there for yeah, so that&#x27;s the equation. In standard form, we just get a X minus. Three have squared. Plus, why my next one people before well, we can read the geometric information off of that pretty easily. Our centers X coordinate is subtracted from X, my center, his wife word and it&#x27;s being practiced for my radius says means weird very so that our center is three halfs one house on our radio assistant.

Ankit Gupta · Answer

in this question. Equation off a circle is given us X squared plus y squared plus four X minus four y minus one equals zero. We have to find center and radios off the circle. For that, we will write the given equation in its standard form by completing the square off X squared plus four X and for Vice Square minus four way. Let&#x27;s relate the creationists X squared plus four x plus y squared minus four y is equal to one now for completing the square off X squared plus four X, we relied four under both sides of the equation and for completing the square off vice terminus for why we relied four on both sides of the equation. No, By simply find this, we will get X plus toe. Whole square bless by minus to hold square is equal to nine, which is three square now. We can compare this with the standard form off the equation, which is X minus. Etch whole squared plus y minus K hold square is equal to our square were at school. McKay&#x27;s, the center and R is the radius. Hence the center off the given equation will be minus do coma do and radius will be three. Now we have to graft the circle for that. First, we will put the center of the circle, which is at minus took on my toe. Now we will consider four points which other? The distance off? Three units from the center. Let&#x27;s take the first point on the right of the center, which will be at one Comotto. And let&#x27;s take one point above the center, which will be at minus Tacoma five and one point on the left off the center, which will be at minus five, comma two and one point below the center, which will be it minus two comma minus one. Now, with the reference off these four points, we can draw a circle. Now we have to find intercepts off the circle. If there are any for finding the X intercept, we will put by equal to zero in the standard form of the equation. This gives us X Plus two whole square plus zero minus two. Whole square, which is four, is equal to three square and that is nine. Hence, X plus two. Whole square is equal to five. Therefore, we can see express to will be equal to plus minus wrote five. Hence the values off xar minus to plus minus root five. Therefore, the X intercepts ar minus two plus minus root five Common zero Now for finding by intercept, we will put X equal to zero in the standard form of the equation. This gives us zero plus two whole square which will before plus y minus two hold square is equal to three square that is nine hence why minus two Whole square will be equal to five. Hence we can say why minus two will be Quito plus minus root five therefore values off wire to plus minus square it off five. Hence, the vie intercepts are zero comma to plus minus root off five.

Harrison Dewhurst · Answer

All right. So to find the center of the race of the circle first, we&#x27;re going to put this equation into stated form. Okay, so we can do that by finding a number that multiplies to one and adds to two. And so that is conveniently gonna be, um X plus one x plus one times x plus one that we&#x27;re also gonna keep the y squared with us and said that equal to four. Okay, so that we can rewrite this expose. One has X plus one squared. Plus why squared eagles for So hopefully Now, that&#x27;s looking more familiar to you as the standard form of on the equation for a circle. So now we can find the radius by looking at this number right over here. But this number is equal to the radius squared. So we have to take the square root of four in this case to find the radius, which is 22 is the radius from the center point of the circle. We can look at this. We have X plus ones. Is this one is being added to the X. That means we&#x27;re gonna be moving left. One unit you can put a minus one for our X coordinate of our center point. And since there&#x27;s nothing being added or subtracted to the Y, that means we&#x27;re staying still for a vertical shift being put a zero.

Ernest Castorena · Answer

this time of year was equation X squared plus y squared minus eight X plus eight line minus four is equal to zero. Let&#x27;s say we could Rear Angelis. I get it easier. Tradition is community Nazi. We&#x27;re gonna complete the square for both X and y. So what we&#x27;re gonna do is look at this time divided by two square at a little sides. Well, it&#x27;s a negative four square in which is the 16 vegetable science Over here we have ah, divided by two positive for swear admissible sense of 16 plus 16. And now and the next step would be able to expand this factory next, minus first word. Yeah, plus why plus four squared. Yeah, and then is equal. Teoh 36 on the right. We&#x27;ll expand to make sure we get an X squared minus four x minus four Explosive. 16 Harry to get a y sport plus four y plus for why I was 16. Okay, so that works out well. And then we could be right the slightly to make it easier to read. But it&#x27;s already in Santa&#x27;s form. Never next minus four square. Why I minus negative one. Where is equal to six and now we could see for a center. The X coordinate is being subtracted from ex wife Ward and detracted from where And the radius is on the right hand side being square so that I read your center is for negative for on my radius and six.

Problem

$f(x)=x^{3}, \quad \frac{f(a+h)-f(a)}{h}$

Problem 29 Hard Difficulty

Answer

Related Courses

Barron's SAT

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter

Video Transcript

Sharon Green & Ira Wolf

Barron's SAT

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Barron's SAT

Sharon Green & Ira WolfBarron's SAT

Sharon Green & Ira Wolf

Barron's SAT