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

• Feb 11th 2008, 07:27 PM
wickwiki
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?
• Feb 11th 2008, 11:29 PM
mr fantastic
Quote:

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?)