What is the condition of tangency of parabola?

let the parabola be y2=4ax and the line be y=mx+c 

then eliminating x we get a quadratic equn as my2-4ay+4ac=0

an if he line is tangent to the parabola then discriminant of the quadratic obtained must be equal to zero

therefore c=a/m this is the required condition of tangent for parabola