The correct option is B L=0 passes through a vertex of the ellipse.
Given parabola : y2=4x
Point (4,4)= (at2,2at)
⇒ t=2 (∵ a=1)
Equation of normal at ′t′ is
y+xt=2at+at3⇒y+2x=12⇒2x+y−12=0
Now, the equation of ellipse is
x236+y220=1
Here,
a2=36, b2=20e2=1−b2a2⇒e=√1−2036=23
Foci =(±ae,0)=(±4,0)
Verticec =(±6,0)
So, L=0 passes through the vertex (6,0)