Chord's length.

Let a tangent $yt = x + at^{2}$ on the given parabola where $a=1$ .

Since it passes from $(1,3)$ therfore the above equation should pass through it and the equation becomes $3t = 1 + t^{2}$ .

solving this qudratic in $t$ we get $t= \frac{3+\sqrt5}{2} = t_1$ and $t = \frac{3-\sqrt5}{2} = t_2$

now we have two values of $t$ and the length of chord on a parabola from $t_1~ and ~t_2$ is $(t_1 - t_2)\sqrt{(t_1 + t_2)^{2} + 4}$ .

putting the value of $t_1 ~and~ t_2$ we get length of chord $=$ $\sqrt65$ $=$ $8.062$