Question

The locus of the point of trisection of all the double ordinates of the parabola $y^2=lx$ is a parabola whose latus rectum is

• A. $\frac{l}{9}$
• B. $\frac{2l}{9}$
• C. $\frac{4l}{9}$
• D. $\frac{l}{36}$

Answer 1

The correct option is A $\frac{l}{9}$

Given ,

the locus of the point of trisection of all the double ordinate of the parabola $y^2=Lx$

also given, to find out the Latus spection for the given parabola.

as we know that

$y^2=4ax$ is the parabola equation.

Let us now equate it with given equation

$4ax=Lx$

$\Rightarrow 4a=L$

$A(a{t}^2,2at)$

$\therefore$ we get $h=a{t}^2\iff 3k=2at$

by squating on betweens we get

$9k^2=4a^2{t}^2\iff 9k^2=4.a^2.\frac{h}{a}[\because h=a{t}^{2}t=h/a$

$\Rightarrow 9k^2=4ah\iff k^2=\frac{4}{9}a.h$

$\because y^2=L.x=\frac{4a}{9}.x\iff y^2=\frac{L}{9}$ Option $\left[A\right]$