lets say x and y satisfy the following relation:
y^2= 4ax which so happens to be a parabola.
now here y belongs to real numbers and x is positive. so let us define a new variable (parameter) t such that t= y/2a or y=2at. obviously we can define any variable like this. now y^2= 4a^2t^2= 4ax or x= 2at^2. hence, we have expressed x and y in terms of a common paramter t so now there is only one variable that we need to deal with. the parametric form of the equation of a tangent can now be easily derived taking a point P(t)= (2at, at^2), and writing the slope point form of line at P. now you might ask how will we get the slope here. well since it is a tangent, we know that m= dy/dx= (dy/dt)/(dx/dt)= 2a/2at= 1/t.
kindly approve :)
