Question

What is the standard form of the equation for this circle?

Answer 1

@hotguy
@Vocaloid
@ any one who can help me

Answer 2

The standard form of a circle is \((x-h)^2+(y-k)^2=r^2\) where the center of the circle is \((h, k)\) and \(r\) is the radius. Can you take it from there?

Answer 3

okay so then that would mean it is (x-4)^2 + (y+5)^2 = 5.5^2

Answer 4

right?

Answer 5

Yup. Great job!

Answer 6

thanks!

Answer 7

np :)

Answer 8

@Calcmathlete could you help me with another question?

Answer 9

Sure

Answer 10

The 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

Answer 11

Do you know how to complete the square?

Answer 12

no

Answer 13

Ok, 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.\[x^2-4x+5=10\] Now, of course, the easiest thing would be to factor, but let's try completing the square instead.\[x^2-4x+\_\_=5\] You're trying to find the number that should go there to make it a perfect square trinomial.\[x^2-4x\color{red}{+4}=5\color{red}{+4}\]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.\[(x-2)^2=9\]That is called completing the square. Does that make sense so far?

Answer 14

kind of, yes

Answer 15

okay now what?

Answer 16

Alright, 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.\[(x-h)^2+(y-k)^2=r^2\]where \(h=-\frac C2\), \(k=-\frac D2\), \(r^2=-E+\left(\frac C2\right)^2+\left(\frac D2\right)^2\)

Answer 17

If you're not quite 100% on completing the square yet, ^ is going to be a bit hard to follow.

Answer 18

okay i kinda follow its a bit hazy but its there

Answer 19

Alright, 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.

Answer 20

okay yeah that does

Answer 21

the only problem is thats not an answer

Answer 22

What is the answer according to your source?

Answer 23

these are our options

Answer 24

With 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?

Answer 25

yeah i copy and paste it

Answer 26

I 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...

Answer 27

i chose e

Answer 28

http://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.

Answer 29

The +10 one is clearly smaller than the +5 one, and the centers stayed the same.

Answer 30

Sorry for all the confusion.

Answer 31

its okay thanks tho

Answer 32

np