suppose the curve is the graph of y=x^2, A(x1,y1). Suppose the tangent point is P(x0,y0), then the equation of the tangent line

is y0+y=2*x0*x. Since A is on this line, y0+y1=2*x0*x1. Together with the equation y0=x0^2, you can solve them and get the value of (x0,y0)