Encontrar el valor del radio y centro de la siguiente ecuación?

<img src="https://tex.z-dn.net/?f=5%20x%5E%7B2%7D%2B5%20y%5E%7B2%7D-10x-20y%2B5%3D0%20%20" />

Dividimos para 5

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5%20x%5E%7B2%7D%20%7D%7B5%7D%2B%20%5Cfrac%7B5y%5E%7B2%7D%20%7D%7B5%7D-%20%5Cfrac%7B10x%7D%7B5%7D-%20%5Cfrac%7B20y%7D%7B5%7D%2B%20%5Cfrac%7B5%7D%7B5%7D%3D0%20%20%20%20%20" />

<img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2By%20%5E%7B2%7D-2x-4y%2B1%3D0%20" />

Agrupamos los términos con la variable x

<img src="https://tex.z-dn.net/?f=%28%20x%5E%7B2%7D-2x%2B........%29%2B%28y%5E%7B2%7D-4y%2B......%29%3D-1%20%20%20%20" />

completamos el trinomio sacamos la mita de - 2x y - 4y y luego elevamos al cuadrado

<img src="https://tex.z-dn.net/?f=%28x%5E%7B2%7D-2x%2B%281%29%5E%7B2%7D%20%29%2B%28y%5E%7B2%7D-4y%2B%282%29%5E%7B2%7D%29%3D-1%2B1%5E%7B2%7D%2B2%5E%7B2%7D%20%20%20%20%20" />

<img src="https://tex.z-dn.net/?f=%28%20x%5E%7B2%7D-2x%2B1%29%2B%28y%5E%7B2%7D-4y%2B4%29%3D-1%2B1%2B4%20%20" />

<img src="https://tex.z-dn.net/?f=%28x-1%29%5E%7B2%7D%2B%28y-2%29%5E%7B2%7D%3D4%20%20" /> ↓ ↓ ↓ h k r²

Centro C(h, k)

<img src="https://tex.z-dn.net/?f=h%3D-%28-1%29%3D1............k%3D-%28-2%29%3D2" />

<img src="https://tex.z-dn.net/?f=r%20%5E%7B2%7D%3D4" />

<img src="https://tex.z-dn.net/?f=r%3D%20%5Csqrt%7B4%7D%3D2%20" />

Sol.

C(1, 2) y r = 2u.