The correct option is D a point circle for k=0
Here (x−a)2+(y−b)2=k(px+qy+r)2 represents conic with (a,b) as focus and px+qy+r=0 as directrix
(x−a)2+(y−b)2=k(p2+q2)(px+qy+r√p2+q2)2
Here e2=k(p2+q2)
For ellipse
0<e2<1⇒0<k(p2+q2)<1⇒0<k<1p2+q2
For parabola,
e2=1⇒k=1p2+q2
For hyperbola,
e2>1⇒k>1p2+q2
For k=0,(x−a)2+(y−b)2=0⇒(x,y)=(a,b) a point circle