If the focus of a parabola and the equations of two perpendicular tangents at any two points $P$ and $Q$ on the parabola are given, can we find the equation of the given parabola?
If not, what information can we get from the parabola? (Like length or equation of the Latus rectum, etc)
If the above can be done, is there somewhat of a generalisation when the two tangents are inclined at an angle $\theta$ to each other?
Any hint or a solution would be much appreciated.