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Question

Locus of mid-points of all chords of the parabola y2=4x which are drawn through the vertex is

A
y2=8x
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B
y2=2x
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C
x2+4y2=16
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D
x2=2y
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Solution

The correct option is B y2=2x
R.E.F image

Q(at2,2at)

P(x,y) be the mid pt.

P(at22,at)

Thus, x=at22 y=at

y2=a2t2

y2=a22xa

y2=2ax

a=1 y2=2x

1170999_1270996_ans_247f3c175f3b4afda44265d6d9d93876.jpg

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