词条 | orthogonal trajectory |
释义 | orthogonal trajectory mathematics ![]() ![]() In two dimensions, a family of curves is given by the function y=f(x,k), in which the value of k, called the parameter, determines the particular member of the family. Two lines are orthogonal, or perpendicular, if their slopes are negative reciprocals of each other. Curves are said to be perpendicular if their slopes at the point of intersection are perpendicular. Depending on context, the slope may also be called the tangent or the derivative, and it can be found using differential calculus (analysis). This derivative, written as y′, will also be a function of x and k. Solving the original equation for k in terms of x and y and substituting this expression into the equation for y′ will give y′ in terms of x and y, as some function y′=g(x,y). ![]() ![]() y2+(x2/2)=k, which represents a family of ellipses (ellipse) orthogonal to the family of parabolas. |
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