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Question

If the locus of mid point of the chords of the parabola y2=4ax which passes through a fixed point (h,k) is also a parabola, then length of its latus rectum (in units) is

A
4a
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B
8a
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C
6a
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D
2a
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Solution

The correct option is D 2a
Equation of chord having P(x1,y1) as mid point is
T=S1
yy12a(x+x1)=y214ax1
It passes through (h,k)
ky12a(h+x1)=y214ax1
Locus of P is
y2ky2ax+2ah=0(yk2)2=2a(x+k28ah)
Length of latus rectum =2a units

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