Which of the following are true for a parabola with focus at S(2, 3) and having the lines x – y = 0 and x + y = 0 as two of its tangents.

The feet of perpendiculars from S(2, 3) to given tangents, are 

$A=(\frac{5}{2},\frac{5}{2}) ,B=(\frac{-1}{2},\frac{1}{2})$
$\therefore$ equation of tangent at vertex is equation of AB = 4x – 6y + 5 = 0. 
Given tangents as perperpendicular. 

The point of itnersection of  perpendicular tangents, lies on directrix which is passing through the point (0,0)

Distance from focus to tangent at vertex is a and 4a is latus rectum.

a=$\frac{5}{2\sqrt{13}}$ 

L.L.R=$\frac{10}{\sqrt{13}}$
Also semi latus rectum is HM of focal segments.