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anonymous
 one year ago
What is the standard form of the equation for this circle?
anonymous
 one year ago
What is the standard form of the equation for this circle?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@hotguy @Vocaloid @ any one who can help me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The standard form of a circle is \((xh)^2+(yk)^2=r^2\) where the center of the circle is \((h, k)\) and \(r\) is the radius. Can you take it from there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so then that would mean it is (x4)^2 + (y+5)^2 = 5.5^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Calcmathlete could you help me with another question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The equation of a circle is x2 + y2 + Cx + Dy + E = 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients C, D, and E affected? i dont get how to work with circles

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know how to complete the square?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, completing the square is kind of a technique that is similar to factoring (somewhat). It's based on the formula \[(a\pm b)^2=a^2\pm2ab+b^2\] The idea is that you're trying to get a quadratic into a form that can become a perfect square. Before we work on your question, let's work with the idea first.\[x^24x+5=10\] Now, of course, the easiest thing would be to factor, but let's try completing the square instead.\[x^24x+\_\_=5\] You're trying to find the number that should go there to make it a perfect square trinomial.\[x^24x\color{red}{+4}=5\color{red}{+4}\]We added 4 on the left side to make it the perfect square trinomial (this is to make it fit the form above). However, to balance the equation, we need to add 4 to the right side as well.\[(x2)^2=9\]That is called completing the square. Does that make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, so what we need to do is complete the square for the equation of the circle above. \[x^2+y^2+Cx+Dy+E=0\]\[(x^2+Cx+\_\_)+(y^2+Dy+\_\_)=E\]\[\left(x^2+Cx+\left(\frac{C}{2}\right)^2\right)+\left(y^2+Dy+\left(\frac D2\right)^2\right)=E+\left(\frac C2\right)^2+\left(\frac D2\right)^2\]\[\left(x+\frac C2\right)^2+\left(y+\frac D2\right)^2=E+\left(\frac C2\right)^2+\left(\frac D2\right)^2\]This should look familiar from the form above.\[(xh)^2+(yk)^2=r^2\]where \(h=\frac C2\), \(k=\frac D2\), \(r^2=E+\left(\frac C2\right)^2+\left(\frac D2\right)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you're not quite 100% on completing the square yet, ^ is going to be a bit hard to follow.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay i kinda follow its a bit hazy but its there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, I'll go over completing the square in a sec again, but to finish up your question, the variables that affect the center of the circle are C and D. Your question asked that if r decreased, how would C, D, E be affected if the center of the circle didn't change. So, since the center didn't move, C and D stay constant. However, E needs to increase for the radius to decrease. Does that make sense? I'll go back to completing the square after this.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the only problem is thats not an answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the answer according to your source?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0these are our options

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0With the way the question is written, I don't think any of the choices are correct. Are you sure that's the exact wording of the question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah i copy and paste it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just double checked everything on my paper. I think their question is just straight up wrong. If it were  E or something instead of + E, then the choice would be on there. I'd just go with the last option since it's the closest one, but...wow...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%2B6x%2B6y%2B5%3D0 http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%2B6x%2B6y%2B10%3D0 Also, ^ that is why I'm sure that their question is flawed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The +10 one is clearly smaller than the +5 one, and the centers stayed the same.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry for all the confusion.
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