the equation x^2 = 4ay represents a one parameter family of parabolas. find an equation of another one parameter family of curves such that at any point (x,y) there is a curve of each family through it and the tangent lines to the two curves at this point are perpendicular. (hint: first show that the slope of the tangent line at any point (x,y), not on the y-axis of the parabola of the given family through that point is 2y/x). this one is really confusing. I don't know where to start.

Question