Please confirm that I am right

[lo2]

We have got:

$$x^2+4x+y^2+y+4=0$$

Which we have to rewrite so that it becomes the formula of the circle and then determine the coordinates of the center of the circle and the radius.

So I do the following:

$$x^2+4x+y^2+y+4=0 \Leftrightarrow x^2+4x+4+y^2+y+\frac{1}{2}=\frac{1}{2}\Leftrightarrow (x+2)^2+(y+\frac{1}{2})^2$$

Then the center has got the following coordinates (-2,-½) and the radius is $$\frac{1}{\sqrt{2}}$$

The book however says something diffrent but am I right?

 

[Random333]

We have got:

$$x^2+4x+y^2+y+4=0$$

Which we have to rewrite so that it becomes the formula of the circle and then determine the coordinates of the center of the circle and the radius.

So I do the following:

$$x^2+4x+y^2+y+4=0 \Leftrightarrow x^2+4x+4+y^2+y+\frac{1}{2}=\frac{1}{2}\Leftrightarrow (x+2)^2+(y+\frac{1}{2})^2$$

Then the center has got the following coordinates (-2,-½) and the radius is $$\frac{1}{\sqrt{2}}$$

The book however says something diffrent but am I right?

.5 times .5 does not equal .5, so that answer can not be right.

 

[Edgardo]

$$x^2+4x+y^2+y+4=0 \Leftrightarrow x^2+4x+4+y^2+y+\frac{1}{2}=\frac{1}{2}\Leftrightarrow (x+2)^2+(y+\frac{1}{2})^2$$

You made a mistake in the last step. Check again what's
$$(y+\frac{1}{2})^2$$.

And you forgot to write the equal sign in the last step.

 

[lo2]

I am a n00b. Why do I make such stupid mistakes those are mistakes that n00bs would make. I just cannot stand making such stupid mistakes please someone help me get rid of the n00bness.

 

[Galileo]

Screwing up is a good thing in this case. Just learn from your mistakes, so you don't make `m again. Practice a lot so you can make lots of mistakes to learn from. The difference between n00b and and someone who's mastered the material is that the master has already made all the mistakes in the past, so he doesn't make them again.