Standard Form equation of a circle (Center-Radius Form): (x−a)2+(y−b)2=r2Where "a" and "b" are the coordinates of the center and "r" is the radius of the circle
2x2+2y2−4x+5y+1=0
Divide through by 2
= x2+y2−2x+52y+12=0
=x2−2x+y2+52y=−12
=x2−2x+12+y2+52y+(54)2−1−2516=−12
=(x−1)2+(y+54)2=−12+1+2516
=(x−1)2+(y−(−54))2=3316
=(x−1)2+(y−(−54))2=(3√34)2
∴a=1,b=−54and r3√34(answer)