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. $y^2=8ax$

Answer 1

Answer: (A)

$2y^2=9ax$

Given equation of parabola is
$y^2=4ax$
A point on the parabola can be written in the parametric form as $(a{t}^2,2at)$
The equation of the tangent to parabola at the point "t" is
$ty=x+a{t}^2$ ....(1)
The equation of the tangent to parabola at the point "2t" is
$2ty=x+4a{t}^2$ ....(2)
Solving (1) and (2), we get
$x=2a{t}^2$
Put this value in (1), we get
$y=3at$
Point of intersection of tangents is $(2a{t}^2,3at)$
On substituting value of $t$, we get $2y^2=9ax$.