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Question

The locus of the mid-point of the line segment joining the focus of the parabola y2=4ax to a moving point of the parabola, is another parabola whose directrix is:

A
x=a
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B
x=0
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C
x=a2
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D
x=a2
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Solution

The correct option is B x=0
Any point on the parabola y2=4ax be (at2,2at)
Let mid point of focus and variable point be (h,k)
h=at2+a2,k=2at+02
t2=2haa and t=ka
k2a2=2haa
Locus of (h,k) is y2=a(2xa)
y2=2a(xa2)
Its directrix is
xa2=a2x=0

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