Parabola 1 Question 6

6. Let (x,y) be any point on the parabola y2=4x. Let P be the point that divides the line segment from (0,0) to (x,y) in the ratio 1:3. Then, the locus of P is

(2011)

(a) x2=y

(b) y2=2x

(c) y2=x

(d) x2=2y

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Answer:

Correct Answer: 6. (a)

Solution:

  1. By section formula,

h=x+04,k=y+04x=4h,y=4k(0,0)Oy2=4x

Substituting in y2=4x,

(4k)2=4(4h)k2=h

or y2=x is required locus.



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