Show that the locus of a point that divi...

Show that the locus of a point that divides a chord of slope `2` of the parabola `y^2 = 4x` internally in the ratio `1:2` is parabola. Find the vertex of this parabola.

A

`((2a)/(9),(8a)/(3))`

B

`((8a)/(9),(2a)/(9))`

C

`((2a)/(9),(8a)/(9))`

D

None of these

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The correct Answer is:

C

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