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Cone Or cyIgurface(25 point) Find the centre and radius of the circle given by the equations22 +y? + 22 63 Ay 122 36 = 0 ; I+ 2y 22 = 1AckoFCoCQaAccoan ondeunnos...

Question

Cone Or cyIgurface(25 point) Find the centre and radius of the circle given by the equations22 +y? + 22 63 Ay 122 36 = 0 ; I+ 2y 22 = 1AckoFCoCQaAccoan ondeunnos

Cone Or cyI gurface (25 point) Find the centre and radius of the circle given by the equations 22 +y? + 22 63 Ay 122 36 = 0 ; I+ 2y 22 = 1 Acko FCoC Qa Accoan ondeunnos



Answers

Find the center and radius of the circle with the given equations. $$ \left(x-\frac{1}{2}\right)^{2}+\left(y-\frac{1}{3}\right)^{2}=\frac{9}{25} $$

Find the center and the radius of cancer. Our equation is X squared plus one squared minus 10 picks plus six. Way 22 is equal to Seo. So we're gonna group are accessing wise together. So we have X squared. When I missed 10 X and he was face plus y squared. That's 61 leave a space equals We're gonna take this 22 to the other site so it becomes making of 22. Then we're gonna take half of these coefficients if I wait, too. And that's where they could have tended. What about two? It's making a fight negative. Five squared is 25. So plus 20 plane here. And plus, when you do the same thing to this coefficient 69 by two and it split 61 by two or three third, it's nine. So we're gonna put last night here and you So now we can rewrite this as X minus place where plus why? Plus three square ukuleles. And then we're gonna take negative 22 and 25. And at my you get what? So the center of my circle is that fine? Make it three opposite of minus Phi this way instead of plus three is Minister or the Radius wouldn't squarely 12. So we're gonna break down 12 into four times. Three squared toys too. And they cancel. Profess were three. So my radius too square receptor.

State, the center and the radius of the circle with the given our equation is X minus 1/2. I swear less. Why? Minus one, I swear equals 9/25. The center of the circle. Take the opposite of these numbers. Is that 1/2? 1/3 the radius willing to take the square root of this number squared, minus three squared 25 5 So the radius is three fits.

Okay, so here we have a question of circle so masterful we needed to convert into standard form. Right. So for that Ah, subject 21 both side. So we can right here. Explorer, my anistan X plus y square plus six wise ago to minus 21. Right now here, we needed to do accomplish square board site. So for this term, we needed to add a 25 board side. So here we can write expert, my understand express 25 a year and also 25 on the right side. And for these two times the I needed to wait here. Nine both sides. So had nine both side. Right now for these three terms, we can write your X minus five whole square and with the other three times a week in right y plus three whole square. And you're 25 plus nine minus 21 with physical do 13. Right. So we can write your X minus Phi whole square. Les y plus three. Whole square is a gold toe road toting all square. No comfort in this situation. Rita. Standard form off a circle. So standard form of the circle, which is given by X minus H hold square, les Y minus K. Hold square is a gold who are square. So as you can see, your is equal to five and K is equal to minus three. So the center of disabilities y minus three and you're the radius of the circle, which is route starting. So this is your center, and that is to your radius. Right? So we can a rock. The simple using this center and these radios. Right? So, as you can see from the graph here that the center of the circle ease fire minus three. And you're here. The radius of the circle, which is approximate Do road toting. Right. Thank you.

When we are going to use the standard form of the equation of a circle. In this format, we can see the center of our circle is H. K. And a radius is in this part. This is radius square but we can use it to find our radius. So we need to get our given equation to look like this equation. It needs to be in this form. We're going to do that by completing the square. First step to completing the square for the exes And wise is to isolate the X and y. So we're going to have x squared minus 2.6 X. Leave some room to complete the square. We need y plus y squared minus 5.4. Why leave some room to complete the square? And we want this um negative 1.6 to move to the other side. So we are going to add 1.26 to both sides. So this side now is positive 1.26 I am going to move this circle so that we have room there. Okay to complete the square. We want to make this a perfect square. Try no meal. Perfect square. Try no meals are in the form X squared. Take this be, we're going to take half of it and square it and write it here. So half of negative 2.6 is negative 1.3 and negative 1.3 squared is 1.69 So I'm going to add 1.69 right here. If I add 1.69 to the left side of the equation after also add 1.69 to the right side of the equation to keep our equation balanced. So what we've just created is a polynomial that will factor to be x minus three, quantity squared because negative 1.3 times negative 1.3 is 1.69 A negative 1.3 plus negative 1.3 is negative 2.6. Same process for the wise we're going to take half of the 5.4 and that is negative 2.7. We're going to square that and we get 7 to 9. So we're going to add 7 to 9 to both sides of the equation. This polynomial now factors to be why minus 2.7 quantity squared. And then on our right side we have the 1 to 6 plus the 1.69 plus the 7.29 We get 10.24 So now we have our equation in standard form, we can see that the h value is negative, nope. The x minus is already part of our formula. So the H is positive 1.3. That's the x corner of our center. The K is positive 2.7. Okay, so that's our center. And then we also know that r squared is equal to 10 to 4. Take the square root of both sides. We get are as equal to the positive square root of 10 0.24 which gives us 3.2. So our radius is three point to our centre is 1.3 comma 2.7.


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