The locus of mid points of chords of the parabola y2=8x drawn through the vertex is a parabola whose
lotus rectum = 4
The parabola is as given below,
AB is the chord with A fixed at the vertex of the parabola and
B moving along the parabola.
M(h,k) is the midpoint whose locus has to be found out.
If (x,y) is the point B on the parabola then,
h=x2;k=y2
x=2h;y=2k
since (x,y) lie on y2=8x
⇒(2k)2=8.2h
4k2=16h
k2=4h
∴ Equation of locus,
y2=4x
lotus rectum=4
focus=(1,0)
correct option=(d)