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Find the radius of a circle with the equation:
x2 + y2 – 18x – 14y + 120 = 0

 Aug 27, 2020
 #2
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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)

 

:)

 Aug 27, 2020

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