Question

The locus of the mid point of the focal radii of a variable point moving on the parabola, $y^2=8x$ is a parabola whose

• A. Latus rectum is half the latus rectum of the original parabola
• B. Vertex is $(1,0)$
• C. Directrix is $y-axis$
• D. Focus has the co-ordinates $(2,0)$

Answer 1

Answer: (A), (B), (C)

The correct options are
A Latus rectum is half the latus rectum of the original parabola
B Vertex is $(1,0)$
C Directrix is $y-axis$

Let any point on parabola be $(2t^2,4t)$

focus is $(2,0)$

midpoint is $(1+t^2,2t)$

Locus of midpoint is

$y^2=4(x-1)$

Vertex is $(1,0)$

L.R$=4$

Diretrix is $x-1=-1$ $\Rightarrow$ $x=0$(y-axis)

Focus is $(1,0)$

L.R original parabola $=4\times 2=8$