Find the orthogonal trajectory of the family of curves
My Self Assessment
a) x2 + (y – c)2 = 1 + c2
Solve
Find the curve whose subtangent is of constant length
Find the curve whose subnormal is constant.
The tangent at any point P of a curve meets the axis of X at T. Find the curve for which OP = PT, O being the origin.
Find the orthogonal trajectory of x2 – y2 = a2
Show that ydx – 2xdy = 0
represents a system of parabolas with common axis and tangent at the vertex.
Show that the solution of the general homogenous equation of the first order and degree, is
where v =
Find the curve which passes through origin and is such that the area included between the curve, the ordinate, and the axis of x is k times the cube of that ordinate.
The normal to a curve meets the axis of x at G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.
Find the curve which is such that the portion of the axis of x cut off between the origin and the tangent at any point is proportional to the ordinate of that point.
The rate of decay of radium is proportional to the amount remaining. Prove that the amount remaining at time t is given by where is the amount of radium at t = 0.
