If a chord of a circle  $x^2+y^2=25$ with one

 extremity at   $(4,3)$  subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be 

Let P be the point $(4, 3)$  and$Q (h, k)$   be the other extremity of the chord through $P$. Centre of the circle is the origin $0$. Then$OP$ is perpendicular to $OQ$

$\Rightarrow \frac{k}{h}\times \frac{3}{4}=-1\Rightarrow \frac{k}{h}=-\frac{4}{3}$

which is satisfied by  $(h,k)=(-3,4)$