Question

The locus of the midpoint of the line segment joining the focus to a moving point on parabola $y^2=4ax$ is another parabola with the direction

• A. a
• B. a/2
• C. 0
• D. -a/2

Answer 1

The correct option is C 0

Take any point on the parabola (at2,2at)(at2,2at)

Therefore the mid point (h,k)=(at2+a2,2at+02)(h,k)=(at2+a2,2at+02)

2h=a(t2+1),at=k2h=a(t2+1),at=k

2h=a(k2a2+1)2h=a(k2a2+1)

So,locus is 2xa=y2+a22xa=y2+a2

y2=2a(x−a/2)y2=2a(x−a/2)

Direction : x =−a2+a2=−a2+a2

=0=0 or y axis

Hence C is the correct answer.