The normal lines of a circle pass through the centre of the circle.
Consider the equation of the circle
Since the circle passes through the point so equation of circle becomes
Now differentiating equation of circle (i) with respect to , we have
If is the slope of tangent line at point , then
Slope of normal line at the point is
Now equation of normal at the point using slope point is
Now putting the values in equation (iii), we get the result
This shows that the normal line passes through the centre of the circle.