The correct option is A 8a4+4a2y2+y2(y2−4ax)=0
Equation of chord having P(x1,y1) as its mid points is
T=S1
⇒yy1−2ax=y21−4ax1
⇒y=2ay1x+y1−4ax1y1⋯(1)
Equation of normal will be
y=mx−2am−am3⋯(2)
∵ both the equation represents the same line
∴m=2ay1
and y1−4ax1y1=−2am−am3
⇒y21−4ax1=−y1(4a2y1+8a4y31)⇒y21(y21−4ax1)+4a2y21+8a4=0
Locus of P is 8a4+4a2y2+y2(y2−4ax)=0