The Locus Of A Point Whose Some Of The Distance From The Origin And The Line x = 2 Is 4 Units, Is

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The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is


Correct option is

y2 = –12(x – 3)

Let P(x, y) be the point for which we have to find the locus.

Writed1 = OP = {(– 0)2 + (y – 0)2}1/2 

d2 = distance of P from 

Given d1 + d2 = 4, d12 = (6 – x)  y2 + x2

                      = (6 – x)2 d1 = 4 – d2  

              y2 = –12(x – 3)



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