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Question

The locus of a point (to the right of x=2) whose sum of the distances from the origin and the line x=2 is 4 units, is

A
y2=12(x3)
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B
y2=12(x3)
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C
x2=12(y3)
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D
x2=12(y3)
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Solution

The correct option is A y2=12(x3)
Let the coordinates of the point be (h,k).
Distance of the point from origin
=(h0)2+(k0)2=h2+k2
Distance of the point from the line x2=0 is h2
according to the given condition,
h2+k2+h2=4h2+k2=6h
squaring both sides, we have
h2+k2=36+h212h or k2=12(h3)
The path of the point is y2=12(x3)

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