Question

The locus of the points of trisection of the double ordinates of the parabola $y^2=4ax$ is

• A. $y^2=ax$
• B. $9y^2=4ax$
• C. $9y^2=ax$
• D. $y^2=9ax$

Answer 1

The correct option is B $9y^2=4ax$

Let $PQ$ be a double ordinate of $y^2=4ax$ and let $R(h,k)$ be the point of trisection. Let the coordinates of $p$ be $(x,y)$, then $x=h$ and $y=3k$.
$\because$ Point $(x,y)$ lies on $y^2=4ax$.
$\therefore (3k{)}^2=4a(h)$
Hence, locus of a point $(h,k)$ is
$9y^2=4ax$.