A circle is described on the line joining the points  $(2,-3)$ and $(-4,7)$  as a diameter 

Equation of the circle is  

$\begin{array}{l}(x-2)(x+4)+(y+3)(y-7)=0\\ \Rightarrow x^2+y^2+2x-4y-29=0\end{array}$

Centre is (1, – 2), radius $=\sqrt{34}$

Distance of the centre from the origin is $\sqrt{5}<\sqrt{34}$