If the equation of the tangent at the point P(3,4) on the parabola...

Slope of the tangent is $\dfrac{3}{4} = tan \theta$
Slope of the focal chord through $P\left(3,4\right)$ is $\tan 2\theta = \dfrac{2tan \theta}{1 - ta{n}^{2}\theta}$

i.e. $\tan 2\theta = \dfrac{2\left(\dfrac{3}{4}\right)}{1 - \dfrac{9}{16}} = \dfrac{24}{7}$
Equation of the focal chord through $P$ is \left(y - 4\right) = \dfrac{24}{7}\left(x - 3\right)$<br />Focus is$S\left(\dfrac{11}{6}, 0\right)$<br />Distance of the focus from the tangent is<br />$\dfrac{\left|3\left(\dfrac{11}{6}\right) - 4\left(0\right) + 7\right|}{\sqrt{{3}^{2} + {4}^{2}}} = \dfrac{5}{2} = 2 . 5