what is the lenght of subnormals in the term of differential quotients of any general curve...

Dear Student,

Let P(x,y) be any point on any general curve. PG be a normal to the curve at point P and G be the point of axis axis. Let PN be the lilne perpendicular to x-axis. So the Projection of Tangent (PG) on the x-axis (NG) is the length of subnormal. Now if PT is tangent at P and T be on x-axis. So concider Angle NTP = theta = angle GPN. Therefore, The length of subnormal will be NG = y tan (theta).

Thanks.