One of the important application of the differential equation is to find out the family of curves for which some conditions involving the derivatives are given. For this one can proceed by making use of the following facts. Equation of the tangent at a point (x, y) to the curve `y=f(x)` is given by `Y-y=dy/dx(X-x).` At the X-axis, Y = 0, and `X=x-y/(dy/dx)` At the Y-axis, X = 0, and `Y = y-dy/dx.` Similar things, can be obtained for normals by writing its equation as `(Y-y)dy/dx+X-x=0.`If `y = f(x)` be a curve such questions length of x intercept of tangent is equal to the distance of the point of tangency from x-axis `f(x)` is given by