JEE Advance - Mathematics (1995 - No. 8)
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 a parabola. Find the vertex of this parabola.
The locus is not a parabola.
The locus is a parabola with vertex (1/9, 4/9).
The locus is a parabola with vertex (4/9, 16/9).
The locus is a parabola with vertex (2/9, 8/9).
The locus is a parabola with vertex (8/9, 32/9).