If (5 , 12) and (24, 7) are the foci of a hyperbola passing through the origin, then (where e is eccentricity and LR is Latus Rectum)

We have foci S1(5, 12) and S2(24,7).Hyperbola passes through P(0, 0). ∴PS1−PS2=2a2a=K or 2a=(24−0)2+(7−0)2−122+52=12∴ a=6S1S2=2ae=(24−5)2+(12−7)2=386∴ e=38612 LR=2b2a=2a2e2−1a =2×6386144−1=1216