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Question

Locus of mid points of normal chords of the parabola y2=4ax is :

A
8a4+4a2y2+y2(y24ax)=0
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B
12a4+7a2y2+y2(y24ax)=0
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C
10a4+6a2y2+y2(y28ax)=0
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D
8a4+9a2y2+y2(y27ax)=0
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Solution

The correct option is A 8a4+4a2y2+y2(y24ax)=0
Equation of chord having P(x1,y1) as its mid points is
T=S1
yy12ax=y214ax1
y=2ay1x+y14ax1y1(1)
Equation of normal will be
y=mx2amam3(2)
both the equation represents the same line
m=2ay1
and y14ax1y1=2amam3
y214ax1=y1(4a2y1+8a4y31)y21(y214ax1)+4a2y21+8a4=0
Locus of P is 8a4+4a2y2+y2(y24ax)=0


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