in-3-10-the-coordinates-of-point-p-on-the-circle-with-center-at-c-are-given-write-an-equation-of-e-8

Question

In $3-10$ , the coordinates of point $P$ on the circle with center at $C$ are given. Write an equation of each circle: a. in center-radius form b. in standard form.
$$
P(4,2), C(0,1)
$$

Alice . · Accepted Answer

Hello. So the gold? This problem is to find the equation of the circle in the centre radius form and the standard for him. So the centre radius form is dependent on the center H comma K in the radius comma radius. Are that a reference in that equation? So it must be better to start with that one. So I&#x27;m going to draw it out approximately where the points are so thes centers at zero comma one. So we go over zero me, go up. What? And then the point is at four comma too. So we go over four and we go up to so and work to This is about the re use. So the circle goes a bit like that. So in order to find that radius me to do a bit of Pythagorean theorem and the distance formula. So we go over for in this and we go up one in this. So, uh, the distance would be the square root of 16 plus one which is equal to you. Square 8 16 17. I&#x27;m sorry. And that&#x27;s ah, equal to the radius of the circle. So these enter radius form of this circle would indeed be X uh, x squared because there&#x27;s no H because it zero, uh, plus why minus when cool squared is equal to 17. And if we were Jake saying this standard for him, we would get X squared, plus y squared me. Just finish that squared minus two by plus one is equal to you. 17. And if we bring the 17 over to the other side, we could x squared plus y squared. Yeah, minus two. Why minus 16 is equal to zero. And that is the standard form of this equation. So now we have the two equations of the circle.

James Kiss · Answer

alright. In this question, we are given that, um, a point p is on the circle at zero. To in the center of the circle is at the origin 00 So here&#x27;s a visual of this circle. We&#x27;re asked for two things. First to writing equation in center radius form, center radius form um is when x squared plus y squared equals r squared. And, um, we&#x27;re adding or subtracting two x and Y, depending on the location of the centre. Since the center is at the origin, it is just X squared plus y squared. Nothing added is attracted to X or y, and we&#x27;re equal to R squared. We&#x27;ll have highlighted a radius in red and the radius here would be two and so two squared is for so the center radius for would be X squared plus y squared equals four. Part B is asking for the standard form. Santer form is just equal to zero. So what we need to do is subtract for X squared plus y squared minus four equals zero is your standard form

Alice . · Answer

in this problem, we&#x27;re going to be finding the center radius form and the standard form of the equation of a circle. So we&#x27;re given a point on the Circle P and the center of the Circle Sea. And so, since the center radius form depends on the center of the circle H comma K, and then the radius of the circle are it might be best to start with that one. So let me draw a rough graph of it. So we have the center see at about 4.4 comma two and they sent in the point p at about three homer, too. So we know that the radius of the circle be one. So let me just start writing out the center radius worm. It&#x27;s going to be ex minus four whole squared, plus why minus two Whole squared is equal to the R squared, which is one squared. And so with that, we will expand it into the standard form. We&#x27;ll get X squared minus eight X plus 16 plus y squared minus four way plus for is equal the one. And if we were to combine terms and put it back into the standard form you get X squared plus y squared minus eight x. Let me just read that. A little neater minus four. Why? Plus 19 since we moved that one over and some 16 and four. So we get 20 minus one is 19 is all equal to zero. So visited two importance of the circles. Let your cure was just use the center and the radius in order to find the first equation and then expanded into the 2nd 1

Alice . · Answer

in this problem. We&#x27;re ex divined wth e stand her radius and standard form of a circle, given the point on the circle and the central circle since we the two forms that given below the information. So the center radius form depends on the center, which was which is going to be on the form each comma K and the radius of the circle, which will be given by the point on the circle in relation to the center. Because we know that if the point lies in the circle, it&#x27;ll be it is all points that lie on the circle or equal distance from the center. That&#x27;s just one of the properties. So if we started with the circle centered, that&#x27;s here. Ah, and we went out to the 0.0 comma minus three. We find that the radius is equal to three because that&#x27;s how far we went down the Y axis. And so if we just continue onward, we&#x27;ll find that Ah Thesent er radius Forum falls unders X minus zero cool squared, Plus why minus zero Whole squared is equal to three squared, so that will be X squared. Plus, y squared is equal to nine. And then if we wanted the standard form, we would leave the constant on the right over so we would get X squared. Plus y squared minus nine is equal is here. Let me just label the answers is a and this is B and those were the year two forms that we can write the equation of us are going.

James Kiss · Answer

all right. In this question, we&#x27;re asked to write an equation of a circle so the center radius form of the equation of a circle is X minus. H squared plus y minus K squared equals R Squared or H K is the center of the circle and R is the radius. So in part, A were asked to find the Senate race. We need to know what the radius of the circle is. So if we think about the give, in fact that in this question P is that for a zero and see the center of the circle is at the origin a quick little visual. We got a point at 40 in the center at 00 that would be a radius of four. The center is at 00 so there is nothing we&#x27;re adding or subtracting two X and why it is just X squared plus y squared equals R squared of ours four then were equal to four. Squared, which is 16. That is the center radius form of the equation off the circle for Part B were asked to find the standard form standard formers, and we&#x27;re just equal to zero. So all we need to do is attract the 16 x squared plus y squared minus 16 equals zero

James Kiss · Answer

we&#x27;re looking toe. Find the equation of a circle here in this circle, really need use the distance for me that I find the radius. So here&#x27;s a reminder of what? The distance. What is the difference of your access squared with the difference of your wise coordinate squared and then we square root. That and this problem were given that some point on a circle. His at 11 and at the center of the circle is at 6 13 So the distance between those two points the point on the circle and at the center is your radius. So we use those coordinate points into the distance. Ah, formula. So we could say X two is six minus the first X coordinate. One squared. Plus you&#x27;re why coordinates 13 and one. Their differences squared. Six minus one is five squared, 13 minus one is 12 squared. Five squared was 12. Squared is 169 in the skirt of 1 69 is 13. So the radius of the circle is 13 and nice. Critical. In order to write the equation of the circle, the Senate radius form of a circle. Given that the center is at some HK location is X minus H squared. Plus why minus Kate Squared equals the radius squared. So, in part, I asked us to write the equation of a circle in Senate Radius form in this center is at 6 13 in the radius is at 13. So if the senator is at 6 13 is gonna be X minus six square plus two Y minus 13 square. And we solved for the radios to be 13. So he called 13 square, which is 169. Part B asked for the standard form. So we&#x27;re just gonna algebraic Lee, get this equal to zero and simply everything. So x minus six. Where does the same thing is? Multiply X minus six by itself. Explain it six times X minus six. Close Y minus 13 times itself equals 1 69 X minus six Squared. Um, whatever method you have learned at this point, to multiply these together will be foiling distributing. Maybe you had a technique memorized, but X minus six times X minus six is X squared minus 12. Expose 36 and then for the wise, why squared minus 26 y plus 1 69 is why minus 13 times Y minus 13 and we&#x27;re so equal to 1 69 Rearrange this. You should write your square in terms First X squared. There&#x27;s a positive y squared, Um, and then our x and y terms. So Linus 12 x minus 26. Why? And then if we subtract the 1 69 to both sides, they&#x27;re gone. So there were equal to zero like we need to be. But we still have this positive 36. So plus 36 equals zero. That is part B.

Problem

In $11-19,$ write the equation of each circle. G…

Problem 10 Easy Difficulty

In $3-10$ , the coordinates of point $P$ on the circle with center at $C$ are given. Write an equation of each circle: a. in center-radius form b. in standard form.
$$
P(4,2), C(0,1)
$$

Answer

a) $x^{2}+(y-1)^{2}=17$
b) $x^{2}+y^{2}-2 y-16=0$

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a) $x^{2}+(y-1)^{2}=17$b) $x^{2}+y^{2}-2 y-16=0$

Algebra 2 and Trigonometry

Grace H.

Heather Z.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Heather Z.

Maria G.

Kristen K.

a) $x^{2}+(y-1)^{2}=17$
b) $x^{2}+y^{2}-2 y-16=0$

Ann Xavier Gantert

Algebra 2 and Trigonometry