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Question

The locus of mid points of chords of the parabola y2=8x drawn through the vertex is a parabola whose


A

focus is (2, 0)

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B

lotus rectum = 8

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C

focus is (0, 2)

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D

lotus rectum = 4

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Solution

The correct option is D

lotus rectum = 4


The parabola is as given below,

AB is the chord with A fixed at the vertex of the parabola and

B moving along the parabola.

M(h,k) is the midpoint whose locus has to be found out.

If (x,y) is the point B on the parabola then,

h=x2;k=y2

x=2h;y=2k

since (x,y) lie on y2=8x

(2k)2=8.2h

4k2=16h

k2=4h

Equation of locus,

y2=4x

lotus rectum=4

focus=(1,0)

correct option=(d)


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