The two lines through (2, 3) from which the circle  $x^2+y^2=25$ intercepts chords of length 8 units, have equation   

We know that the length $\text{'}/\text{'}$ of the chord intercepted by the circle $x^2 + y^2 = a^2$ on the straight line $y=mx+c$ is

$l=2\sqrt{\frac{a^2\left(1+m^2\right)-6^2}{1+m^2}}$

Here, $a= 5$ and $y=mx+c$ passes through $(2, 3).$

$\begin{array}{l}\therefore 3=2m+c\Rightarrow c=3-2m.\\ \therefore 2\sqrt{\frac{a^2\left(1+m^2\right)-c^2}{1+m^2}}=8\\ \Rightarrow 2\sqrt{\frac{25\left(1+m^2\right)-(3-2m{)}^2}{1+m^2}}=8\\ \Rightarrow 5m^2+12m=0\Rightarrow m=0,-12/5.\end{array}$

$\Rightarrow c=3\text{ or, }39/5 [\text{ Using }i=3-2m]$ 

Hence, the equations of the required lines are 

$y=3$ and $12x+5y=39$