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Question

# Locus of the point of intersection of tangents at the end points of normal chord of the parabola y2=4ax is

A
xy2+2a(4a2+y2)=0
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B
xy2=2a(2a2+y2)
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C
xy2+a(2a2+y2)=0
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D
xy2=a(2a2+y2)
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Solution

## The correct option is A xy2+2a(4a2+y2)=0Let point of intersection be (x1,y1)Then normal chord is the chord of contact⇒yy1=2a(x+x1)y+t1x=2at1+2at13 is equation of normal chord⇒y11=−2at1=2ax12at1+2at13y1=−2at1 and x1=−2a(1+t12)t1=−2ay1⇒x1=−2a(1+4a2y12)⇒xy12=−2a(y12+4a2)∴ required locus is xy2+2a(y2+4a2)=0

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