Find the radius of a circle with the equation:
x2 + y2 – 18x – 14y + 120 = 0
+1084 Completing the square: a very useful technique.
Hmm..that sounds like a good book title
Anyways, we know that circles are in the form (x−a)^2 + (y−b)^2 = r^2, so how do we get there? By completing the square! (Wow, that rhymes...)
We need to deal with both the x and y.
X:
We see that x^2 - 18x is a fraction of a square. To find the last bit, we divide -18 by 2: this gives us -9. So, we need to take away 81 from 120. This leaves us with: (x−9)^2 + (y−b)^2 + 39 = 0.
Y:
Again, our incomplete square is y^2 - 14y. Divide by 2: -7. Subtract 49: leaves us with -10. Which makes our equation: (x−9)^2 + (y−7)^2 - 10 = 0.
(x−9)^2 + (y−7)^2 - 10 = 0
(x−9)^2 + (y−7)^2 = 10
Therefore, the radius is sqrt(10)
:)
