Let PQ be a focal chord of the parabola y ^ 2 = 36x of length 100,...

We have been given the length of focal chord $PQ = 100$.

Length of focal chord at $\left(t\right) = a{\left(t + \dfrac{1}{t}\right)}^{2} = 100$

Where $a = 9$

$t + \dfrac{1}{t} = \pm \dfrac{10}{3}$

$∴ t = 3, \dfrac{1}{3}, - 3, \dfrac{- 1}{3}$

Since ordinate of $P$ is $+ ve$

∴ t = 3 or $\dfrac{1}{3}$

($t = 3$ as slope of $PQ$ is positive)

$∴ M ( 21, 9 )$

Required line$: y - 9 = \dfrac{- 80}{60} ( x - 21 )$

$⇒ 4x + 3y = 111$

$\left(- 3, 43\right)$ does not lie on line.

Hence this is the correct option.