If one end of focal chord of the parabola y 2 = 8 x is 1 2 , 2 , then the length of the focal chord…

Given parabola is $y^2=8x$

By comparing with parabola $y^2=4ax$

$a = 2$

Parametric point on parabola is $\left(a{t}^2, 2at\right) = \left(2t^2, 4t\right) = \left(\frac{1}{2}, 2\right)$

$\Rightarrow 4t =2$

$t = \frac{1}{2}$

Length of focal chord will be $a{\left(t+\frac{1}{t}\right)}^2$

$= 2{\left(\frac{1}{2}+2\right)}^2$

$= 2 \times \left(\frac{25}{4}\right)$

$=\frac{25}{2}$