# Thread: Center (h,k) and the radius r of each circle.

1. ## Center (h,k) and the radius r of each circle.

OK, I tried doing part of this problem but now I am stuck.

1a. Find the center (h,k) and the radius r of each circle.
$\displaystyle x^2+y^2+4x+2y-20=0$

$\displaystyle x^2+y^2+4x+2y-20=0$

$\displaystyle (x^2+4x)+(y^2+2y)=20$

$\displaystyle (x^2+4x+4)+(y^2+2y+1)=20+4+1$

$\displaystyle (x^2+4x+4)+(y^2+2y+1)=25$

Next Step, what exactly do I do now to solve this?

2. Originally Posted by wickwiki
OK, I tried doing part of this problem but now I am stuck.

1a. Find the center (h,k) and the radius r of each circle.
$\displaystyle x^2+y^2+4x+2y-20=0$

$\displaystyle x^2+y^2+4x+2y-20=0$

$\displaystyle (x^2+4x)+(y^2+2y)=20$

$\displaystyle (x^2+4x+4)+(y^2+2y+1)=20+4+1$

$\displaystyle (x^2+4x+4)+(y^2+2y+1)=25$

Next Step, what exactly do I do now to solve this?
You're kidding? After doing all the hard work you stumble one line from the finish!

Factorise the perfect squares:

$\displaystyle (x + 2)^2 + (y + 1)^2 = 5^2$

Ta da!

(*Ahem* .... it is ta da, right? You do know how to read off the centre and the radius from this?)