Question 1063885
One of the points on this circle is  (9,0), the only point on this circle for which x=0.  The circle has center at  (4,0), so this radius  (of length 5)  from center to x=9 on the circle is perpendicular to the desired tangent line at x=9, which means, this tangent line is vertical, having undefined slope.


The line asked for in the question is  {{{x=9}}}.


No taking of derivative needed.