Question

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

• A. $y^2=ax,$
• B. ${9y}^2=4ax,$
• C. $9y^2=4ax\left(d\right)$
• D. $y^2=9ax$

Answer 1

Answer: (B)

${9y}^2=4ax,$

We have,

Equation of parabola:-

$y^2=4ax$

The point $(a{t}^2,2at)$

Now,

$h=a{t}^2,3k=2at$

Because the point of trisection of double ordinate

By given equation

$y^2=4ax$

$\Rightarrow {\left(3k\right)}^2=4\times a\times h$

$\Rightarrow 9k^2=4ah$

Hence, the locus is $9y^2=4ax$

Hence, this is the answer.