Q.
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2= 4ax is another parabola with directrix
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a
x=−a
b
x = – a/2
c
x = 0
d
x = a/2
answer is C.
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Detailed Solution
The focus of the parabola y2 = 4ax is S (a, 0), let P (at2 , 2at) be any point on the parabola then coordinates of the mid-point of SP are given by x=at2+12, y=2at+02Eliminating ‘t’ we get the locus of the mid-point as y2=2ax−a2 or y2=2a(x−a/2) (1)which is a parabola of the form Y2=4AX (2)where Y=y,X=x−a/2 and A=a/2Equation of the directrix of (2) is X=−ASo equation the directrix of (1) is x−a/2=−a/2⇒x=0
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