Two perpendicular tangents PA and PB are

drawn to $y^2=4ax$ minimum length of AB is equal to $ka$ then the value of $k$ is 

 

We know that the tangents at the ends of a focal

 chord are perpendicular. Thus, the chord of contact

 of perpendicular tangents is a focal chord. Also,

 latusrectum is a focal chord of minimum length.

 Hence, the minimum length of  $AB$  is  $4a$