Explanation

(c)
Given equation of parabola is rewritten as
$169\left\{ (x - 1)^{2} + (y - 3)^{2} \right\} = {(13)}^{2}\left\{ \left( \frac{5x - 12y + 17}{13} \right)^{2}\ ^{\ } \right\}$
$\Rightarrow {(x - 1)}^{2} + {(y - 3)}^{2}\left( \frac{5x - 12y + 17}{13} \right)^{2}$
$\Rightarrow SP = PM$
$\therefore$ Focus is (1, 3) and equation of directrix is
$5x - 12y + 17 = 0$
The distance of the focus from directrix $= \left| \frac{5 - 36 + 17}{\sqrt{25 + 144}} \right| = \frac{14}{13}$
$\therefore$ Length of latusrectum $= 2 \times \frac{14}{13} = \frac{28}{13}$