Answer
$(4+\sqrt 7,2)$ and $(4-\sqrt 7,2)$.
Work Step by Step
Step 1. The equation for a circle with center at $(4,5)$ and radius $4$ can be written as $(x-4)^2+(y-5)^2=16$
Step 2. Use $y=2$ in the above equation to get $(x-4)^2+(2-5)^2=16$ or $(x-4)^2=7$ which gives $x=4\pm\sqrt 7$
Step 3. The points of intersection are $(4+\sqrt 7,2)$ and $(4-\sqrt 7,2)$.
