The correct option is C 121y2=6ax
Let the point P≡(h,k) divides the double ordinate with end points A≡(x,y) and B≡(x,−y) in the ratio 5:6.
Then, h=6x+5x11
⇒x=h ⋯(i)
and k=6y−5y11
⇒y=11k ⋯(ii)
Putting (i) and (ii) in parabola y2=6ax, we get
(11k)2=6a(h)
⇒121k2=6ah
Hence, locus of the point is 121y2=6ax