I learned tangent line as a concept associated with a circle. I thought to make a tangent line, it might have some specific point which is perpendicular to. as always did with circle did. But in the lesson of calculus, it doesn't seems any another point to associate. To draw tangent lines of some graph, how could we refer the slope of tangent line? Before we calculate?
I mean what makes some line to be a tangent line on the graph. How could be a tangent line with out any other point?