Concept:Rewrite the circle equation in the standard form (x−h)2+(y−k)2=r2, then r is the radius.Explanation:Start with 2x2−4x+2y2−6y−2=0.Divide the whole equation by 2:x2−2x+y2−3y−1=0.Move the constant term to the right side:x2−2x+y2−3y=1.Complete the square for x:x2−2x=(x−1)2−1.Complete the square for y:y2−3y=(y−23)2−49.Substitute back:(x−1)2−1+(y−23)2−49=1.(x−1)2+(y−23)2=1+1+49=417.Therefore, r2=417, so r=417=217.Answer:r=217, which is Option D.