Parabolas

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 : ?

[Show your working...I've found the midpoint of the segment in terms of parameter t but I'm not able to advance beyond that..]

2 Answers

mid point --> [a(1+t² ) /2 , at]

Substituting the mid point in that we get

(at)² = 2a [a(1+t² ) /2 - a/2 ]

Y² = 4A[X - c]

A = a/2

X-c = x - a/2

Is the directrix ---> X + a/2 = 0 => x - a/2 + a/2 = 0

x = 0

Uttara..what exactly have you done here?
Yes thats the ans..

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