Circle

The correct option is (B):

The correct option is: B and D

Concept: Intersection of perpendicular diameters is center of circle. Step 1: {\color{red}Find center.} Solve: Add: Center = . Step 2: {\color{red}Distance to origin.} Radius = distance from center to origin:

Concept: Normal to parabola at parameter : Normal to : Step 1: {\color{red}Equate slopes.} For common normal: Step 2: {\color{red}Substitute relation.} Remaining equations lead to cubic in parameter. Two cubics intersect ⇒ up to 6 solutions. Step 3: {\color{red}Maximum count.} Maximum common normals = 6.