Explanation

(d)
Given that equation of parabola is $y^{2} = 9x$
On comparing with $y^{2} = 4ax$, we get $a = \frac{9}{4}$
Now, equation of tangent to the parabola $y^{2} = 9x$ is
$y = mx + \frac{\frac{9}{4}}{m}$ …(i)
If this tangent passing through the point (4, 10), then
$10 = 4m + \frac{9}{4m}$
$\Rightarrow {16m}^{2} - 40m + 9 = 0$
$\Rightarrow (4m - 9)(4m - 1) = 0$
$\Rightarrow m = \frac{1}{4},\ \frac{9}{4}$
On putting the values of $m$ in Eq. (i)
$4y = x + 36$ and $4y = 9x + 4$
$\Rightarrow x - 4y + 36 = 0$ and $9x - 4y + 4 = 0$