Problem 1.42

A particle moves along the plane trajectory \(y(x)\) with velocity \(v\) whose modulus is constant. Find the acceleration of the particle at the point \(x=0\) and the curvature radius of the trajectory at that point if the trajectory has the form (a) of a parabola \(y=a x^{2}\); (b) of an ellipse \((x / a)^{2}+(y / b)^{2}=1 ; a\) and \(b\) are constants here.