The locus of the midpoint of the focal radii of a variable point moving on the…

MATHEMATICS · Multi correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The locus of the midpoint of the focal radii of a variable point moving on the parabola

y^2=4ax

is a parabola whose (1) latus rectum is half the latus rectum of the original parabola (2) vertex is

\left(\frac{a}{2},0\right)

(3) directrix is the

y

-axis (4) focus has coordinates

(a,0)