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Question

The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola y2=4ax is the curve

A
y2(x+2a)4a3=0
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B
y2(x+2a)+4a3=0
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C
y2(x2a)+4a3=0
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D
y2(x2a)4a3=0
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Solution

The correct option is B y2(x+2a)+4a3=0
If (h,k) be the point of intersection of tangents then the equation of chord of contact is ky=2a(x+h)(1)
Equation of normal y=mx2amam3(2)
Since both the equations are same, so by comparing we get,
m=2ak, and
2ahk=2amam3
2ahk=2a(2ak)a(2ak)3
k2(h+2a)=4a3
The required locus is y2(x+2a)+4a3=0

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