Determine the centre and radius of a circle

Given is the following equation of a circle, for which I've to determine its centre and radius. I'm running into some difficulties when I'm trying to complete the squares.

This leads me to believe the centre would be (1, -2). Now to find its radius I'll just complete the squares and simplify:

This obviously isn't correct, -1 being kind of a weird radius (Giggle). So what am I doing wrong here? The correct answer (according to my textbook) should be r=3. I guess I'm missing something with completing the y-part, since -1 + 4 = 3, but can't wrap my head around it...

Any handy tips for solving these kind of exercises?

Re: Determine the centre and radius of a circle

Quote:

Originally Posted by

**Lepzed** Given is the following equation of a circle, for which I've to determine its centre and radius. I'm running into some difficulties when I'm trying to complete the squares.

This leads me to believe the centre would be (1, -2). Now to find its radius I'll just complete the squares and simplify:

This obviously isn't correct, -1 being kind of a weird radius (Giggle). So what am I doing wrong here? The correct answer (according to my textbook) should be r=3. I guess I'm missing something with completing the y-part, since -1 + 4 = 3, but can't wrap my head around it...

Any handy tips for solving these kind of exercises?

Your problem is that you're saying that when it does not. The answer is

In other words once you've completed the square on the LHS you should have and you can then add 5 to both sides to remove the constants: which gives the radius as 3.

Your co-ordinates for the centre of the circle are correct

Re: Determine the centre and radius of a circle

Re: Determine the centre and radius of a circle

I'm practicing some more and stumbled upon the following: describe the region defined by the following pair of inequalities:

I'm having some difficulties interpreting this. At first I thought I could rewrite each inequality to try to make some more sense of it, like so: , but that still doesn't make alot of sense to me.

What I've further tried, is to just write it as a 'normal' equation: , then x & y are , same for . Don't these circles describe exactly the same area?

If not, how should I deal with the 2x and 2y?

Re: Determine the centre and radius of a circle

Quote:

Originally Posted by

**Lepzed**
I'm having some difficulties interpreting this. At first I thought I could rewrite each inequality to try to make some more sense of it, like so:

, but that still doesn't make alot of sense to me.

That system can be rewritten by completing squares.

Those are both the interiors of circles, open disks.