Finding the Center and Radius of a Circle: Analytic Geometry I

[kLownn]

Homework Statement

Find the centre and radius of the circle x²+y²-4x+2y+6=0

I have the solution. The circle is no defined because r² = -1 is impossible.
But... how do I even DO that equation to get the answer -1?!

 

[Dick]

You complete the squares so you can write it in the form (x+a)^2+(y+b)^2=c. Do you know how to do that?

 

[kLownn]

You complete the squares so you can write it in the form (x+a)^2+(y+b)^2=c. Do you know how to do that?

I learned how to do that while I was in school.. I forget how to do it now.. >_<

 

[Dick]

Take the x part. You've got x^2-4x. If I add something to that it will become a perfect square of the form (x-a)^2. What's 'a'? What do you have to add?

 

[kLownn]

Take the x part. You've got x^2-4x. If I add something to that it will become a perfect square of the form (x-a)^2. What's 'a'? What do you have to add?

Oh! Is "a" 2x?
(x-2x)² ?

 

[Dick]

No, no. (x-a)^2=x^2-2ax+a^2, yes? If you match that up with x^2-4x, the 4 must be the 2a, as I see it. Think back to when you did this before.

 

[kLownn]

No, no. (x-a)^2=x^2-2ax+a^2, yes? If you match that up with x^2-4x, the 4 must be the 2a, as I see it. Think back to when you did this before.

Ohh, I see now.. so I just do the same thing for y?

 

[Dick]

Ohh, I see now.. so I just do the same thing for y?

Sure.

 

[kLownn]

Sure.

Thank you so much! :)

 

[icystrike]

Homework Statement

Find the centre and radius of the circle x²+y²-4x+2y+6=0

I have the solution. The circle is no defined because r² = -1 is impossible.
But... how do I even DO that equation to get the answer -1?!

it can actually be express as x²+y²+2fx+2gy+c=0

whrby C(-f,-g) and radius is \sqrt{g²+f²-c}

 

[HallsofIvy]

it can actually be express as x²+y²+2fx+2gy+c=0

whrby C(-f,-g) and radius is \sqrt{g²+f²-c}

No, it isn't. It is much better to actually do the "complete the square" rather than memorize formulas: so you don't make silly mistakes like that.

 

[icystrike]

No, it isn't. It is much better to actually do the "complete the square" rather than memorize formulas: so you don't make silly mistakes like that.

yep (: noted.