Show that the line $3x-4y=25$ and the circle $x^2+y^2=25$ intersect in two coincident points. Show that the line $3x-4y=25$ and the circle $x^2+y^2=25$ intersect in two coincident points. What does two coincident points mean?

If you draw a line through a circle, normally they intersect at two points. The problem is asking you to show that it only intersects at one point. Coincident means "occurring together in space or time", so two possible coincident points are actually one point.