Question

The locus of point of intersection of two tangents to $y^2=4ax$ at $t$ and $2t$ on the parabola is

• A. $2y^2=9ax$
• B. $4y^2=9ax$
• C. $3y^2=4ax$
• D. $3y^2=8ax$

Answer 1

The correct option is A $2y^2=9ax$

Point of intersection of two tangents to $y^2=4ax$ at $t$ and $2t$ is $(2a{t}^2,3at)$
Let $(h,k)$ be the locus
So, $3at=k\Rightarrow t=\frac{k}{3a}$
and $h=2a{t}^2\Rightarrow h=2a{\left(\frac{k}{3a}\right)}^2$
$\Rightarrow 2k^2=9ah$
$\therefore 2y^2=9ax$